Answer: a because you cannot use a point in graphing a linear funtion
Answer: A Step-by-step explanation: There are three basic methods of graphing linear functions. The first is by plotting points and then drawing a line through the points. The second is by using the y-intercept and slope. And the third is by using transformations of the identity function f (x) = x. Thanks! ANSWER THE FOLLOWING QUESTIONS: 1. Which of the following is NOT a method in graphing a linear function? a. using a point b. using x-intercept and y-intercept c. using slope and the y-intercept d. using the slope and a point 2. Which of the following is the hypothesis in the statement? "If you will sleep early, then you will wake up early" a. If you will sleep early b. then you will wake up early c. you will wake up early d. you will sleep early 3. Using the statement "A polygon with exactly 4 sides is a quadrilateral", what kind of statement is this? "If a polygon is quadrilateral, then it has exactly 4 sides" a. Inverse b. converse c. contrapositive d. conditional statement 7. Which of the following is NOT a method in graphing a linear function?
Gauthmath Drag an image here, or Upload a file 2. Which of the following is NOT a method in graphing a linear function? a.using a point b.using x-intercept and y-intercept c. using slope and the y-intercept d. using the slope and a pointQuestion  Gauthmathier7829Grade 12 · 2021-06-20 YES! We solved the question! Check the full answer on App Gauthmath 2. Which of the following is NOT a method in graphing a linear function? HenryAnswer Thanks (126) Feedback from students Does the answer help you? Rate for it! Learning Outcomes
We previously saw that that the graph of a linear function is a straight line. We were also able to see the points of the function as well as the initial value from a graph. There are three basic methods of graphing linear functions. The first is by plotting points and then drawing a line through the points. The second is by using the y-intercept and slope. The third is applying transformations to the identity function [latex]f\left(x\right)=x[/latex]. Graphing a Function by Plotting PointsTo find points of a function, we can choose input values, evaluate the function at these input values, and calculate output values. The input values and corresponding output values form coordinate pairs. We then plot the coordinate pairs on a grid. In general we should evaluate the function at a minimum of two inputs in order to find at least two points on the graph of the function. For example, given the function [latex]f\left(x\right)=2x[/latex], we might use the input values 1 and 2. Evaluating the function for an input value of 1 yields an output value of 2 which is represented by the point (1, 2). Evaluating the function for an input value of 2 yields an output value of 4 which is represented by the point (2, 4). Choosing three points is often advisable because if all three points do not fall on the same line, we know we made an error. How To: Given a linear function, graph by plotting points.
Example: Graphing by Plotting PointsGraph [latex]f\left(x\right)=-\frac{2}{3}x+5[/latex] by plotting points. Try ItGraph [latex]f\left(x\right)=-\frac{3}{4}x+6[/latex] by plotting points. Graphing a Linear Function Using y-intercept and SlopeAnother way to graph linear functions is by using specific characteristics of the function rather than plotting points. The first characteristic is its y-intercept which is the point at which the input value is zero. To find the y-intercept, we can set [latex]x=0[/latex] in the equation. The other characteristic of the linear function is its slope, m, which is a measure of its steepness. Recall that the slope is the rate of change of the function. The slope of a linear function is equal to the ratio of the change in outputs to the change in inputs. Another way to think about the slope is by dividing the vertical difference, or rise, between any two points by the horizontal difference, or run. The slope of a linear function will be the same between any two points. We encountered both the y-intercept and the slope in Linear Functions. Let’s consider the following function. [latex]f\left(x\right)=\frac{1}{2}x+1[/latex] The slope is [latex]\frac{1}{2}[/latex]. Because the slope is positive, we know the graph will slant upward from left to right. The y-intercept is the point on the graph when x = 0. The graph crosses the y-axis at (0, 1). Now we know the slope and the y-intercept. We can begin graphing by plotting the point (0, 1) We know that the slope is rise over run, [latex]m=\frac{\text{rise}}{\text{run}}[/latex]. From our example, we have [latex]m=\frac{1}{2}[/latex], which means that the rise is 1 and the run is 2. Starting from our y-intercept (0, 1), we can rise 1 and then run 2 or run 2 and then rise 1. We repeat until we have multiple points, and then we draw a line through the points as shown below. A General Note: Graphical Interpretation of a Linear FunctionIn the equation [latex]f\left(x\right)=mx+b[/latex]
[latex]m=\frac{\text{change in output (rise)}}{\text{change in input (run)}}=\frac{\Delta y}{\Delta x}=\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}[/latex] Q & ADo all linear functions have y-intercepts? Yes. All linear functions cross the y-axis and therefore have y-intercepts. (Note: A vertical line parallel to the y-axis does not have a y-intercept. Keep in mind that a vertical line is the only line that is not a function.) How To: Given the equation for a linear function, graph the function using the y-intercept and slope.
Example: Graphing by Using the y-intercept and SlopeGraph [latex]f\left(x\right)=-\frac{2}{3}x+5[/latex] using the y-intercept and slope. Try ItFind a point on the graph we drew in Example: Graphing by Using the y-intercept and Slope that has a negative x-value. Graphing a Linear Function Using TransformationsAnother option for graphing is to use transformations on the identity function [latex]f\left(x\right)=x[/latex]. A function may be transformed by a shift up, down, left, or right. A function may also be transformed using a reflection, stretch, or compression. Vertical Stretch or CompressionIn the equation [latex]f\left(x\right)=mx[/latex], the m is acting as the vertical stretch or compression of the identity function. When m is negative, there is also a vertical reflection of the graph. Notice that multiplying the equation [latex]f\left(x\right)=x[/latex] by m stretches the graph of f by a factor of m units if m > 1 and compresses the graph of f by a factor of m units if 0 < m < 1. This means the larger the absolute value of m, the steeper the slope. Vertical stretches and compressions and reflections on the function [latex]f\left(x\right)=x[/latex]. Vertical ShiftIn [latex]f\left(x\right)=mx+b[/latex], the b acts as the vertical shift, moving the graph up and down without affecting the slope of the line. Notice that adding a value of b to the equation of [latex]f\left(x\right)=x[/latex] shifts the graph of f a total of b units up if b is positive and |b| units down if b is negative. This graph illustrates vertical shifts of the function [latex]f\left(x\right)=x[/latex]. Using vertical stretches or compressions along with vertical shifts is another way to look at identifying different types of linear functions. Although this may not be the easiest way to graph this type of function, it is still important to practice each method. How To: Given the equation of a linear function, use transformations to graph the linear function in the form [latex]f\left(x\right)=mx+b[/latex].
Example: Graphing by Using TransformationsGraph [latex]f\left(x\right)=\frac{1}{2}x - 3[/latex] using transformations. Try ItGraph [latex]f\left(x\right)=4+2x[/latex], using transformations. Q & AIn Example: Graphing by Using Transformations, could we have sketched the graph by reversing the order of the transformations? No. The order of the transformations follows the order of operations. When the function is evaluated at a given input, the corresponding output is calculated by following the order of operations. This is why we performed the compression first. For example, following order of operations, let the input be 2. [latex]\begin{array}{l}f\text{(2)}=\frac{\text{1}}{\text{2}}\text{(2)}-\text{3}\hfill \\ =\text{1}-\text{3}\hfill \\ =-\text{2}\hfill \end{array}[/latex] Contribute!Did you have an idea for improving this content? We’d love your input. Improve this pageLearn More What are the methods in graphing a linear function?There are three basic methods of graphing linear functions. The first is by plotting points and then drawing a line through the points. The second is by using the y-intercept and slope. And the third is by using transformations of the identity function f(x)=x.
What are the 4 types of linear functions?Summary. Students learn about four forms of equations: direct variation, slope-intercept form, standard form and point-slope form.
What are the four methods in graphing linear equations?A solutions to a system of equations are the point where the lines intersect. There are four methods to solving systems of linear equations: graphing, substitution, elimination and matrices.
Which of the following is a not a linear function?The answer is c.
The function 2X + 5YZ is not a linear function since it contains a product of variables.
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Which of the following is not a method in graphing a linear function
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