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As stated in the problem the line is horizontal. This means that its slope is zero. Mathematically it means that it is a line parallel to the x-axis and passing through y = -3 as shown below as horizontal line 1. The horizontal line 1 passing through the point (2, -3) is represented by the equation y = -3. There is another horizontal line 2 which is passing through the point (1,2) which also has slope zero as it is parallel to the x-axis and represented by the equation y = 2 What is the equation of the horizontal line that passes through the point (2, -3)?Summary: The equation of the horizontal line that passes through the point (2, -3) is y = -3 Explanation:Begin by finding the slope of the line using the formula #m = (y_2-y_1)/(x_2-x_1)# For the points #x_1 = 2# #m = (-3-(-3))/(1-2)# #m=0/-1# #m=0# This equation is actually a horizontal line running through the y axis at #y=-3# Solution : Let the equation of straight line be `(x)/(a)+(y)/(b)=1`. <br> It passes through the point `(2,3)` <br> `(2)/(a)+(3)/(b)=1`…..`(1)` <br> Given that `a+b=10` <br> `implies b=10-a` <br> From eq. `(1)` <br> `(2)/(a)+(3)/(10-a)=1` <br> `implies (20-2a+3a)/(a(10-a))=1` <br> `implies20+a=10a-a^(2)` <br> `implies a^(2)-9a+20=0` <br> `implies (a-4)(a-5)=0` <br> `implies a=4` or `a=5` <br> If `a=4` then `b=10-4=6` <br> If `a=5` then `b=10-5=5` <br> Therefore, equation of line is <br> `(x)/(4)+(y)/(6)=1` or `(x)/(5)+(y)/(5)=1` <br> `implies 3x+2y=12` or `x+y=5` First, let's see it in action. Here are two points (you can drag them) and the equation of the line through them. Explanations follow. ../geometry/images/geom-line-equn.js The PointsWe use Cartesian Coordinates to mark a point on a graph by how far along and how far up it is:
StepsThere are 3 steps to find the Equation of the Straight Line :
Step 1: Find the Slope (or Gradient) from 2 PointsWhat is the slope (or gradient) of this line? We know two points:
The slope is the change in height divided by the change in horizontal distance. Looking at this diagram ... Slope m = change in ychange in x = yA − yBxA − xB In other words, we:
Like this: m = change in y change in x = 4−3 6−2 = 1 4 = 0.25 It doesn't matter which point comes first, it still works out the same. Try swapping the points: m = change in y change in x = 3−4 2−6 = −1 −4 = 0.25 Same answer. Step 2: The "Point-Slope Formula"Now put that slope and one point into the "Point-Slope Formula" Start with the "point-slope" formula (x1 and y1 are the coordinates of a point on the line): y − y1 = m(x − x1) We can choose any point on the line for x1 and y1, so let's just use point (2,3): y − 3 = m(x − 2) We already calculated the slope "m": m = change in ychange in x = 4−36−2 = 14 And we have: y − 3 = 14(x − 2) That is an answer, but we can simplify it further. Step 3: SimplifyStart with:y − 3 = 14(x − 2) Multiply 14 by (x−2):y − 3 = x4 − 24 Add 3 to both sides:y = x4 − 24 + 3 Simplify:y = x4 + 52 And we get: y = x4 + 52 Which is now in the Slope-Intercept (y = mx + b) form. Check It!Let us confirm by testing with the second point (6,4): y = x/4 + 5/2 = 6/4 + 2.5 = 1.5 + 2.5 = 4 Yes, when x=6 then y=4, so it works! Another ExampleExample: What is the equation of this line?Start with the "point-slope" formula: y − y1 = m(x − x1) Put in these values:
And we get: y − 6 = −2(x − 1) Simplify to Slope-Intercept (y = mx + b) form: y − 6 = −2x + 2 y = −2x + 8 DONE! The Big ExceptionThe previous method works nicely except for one particular case: a vertical line: A vertical line's gradient is undefined (because we cannot divide by 0): m = yA − yBxA − xB = 4 − 12 − 2 = 30 = undefined But there is still a way of writing the equation: use x= instead of y=, like this: x = 2 7270, 525, 526, 1165, 1166, 7291, 7292, 7300, 7301, 7302 What is an equation of the line that passes through the point (Summary : The equation of the line that passes through (-2, 3) and is parallel to 2x + 3y = 6 is 2x + 3y - 5 = 0.
What is an equation of the line that passes through the point (y - 3 = m(x+2 ) Or y = m(x+2) + 3 is the line that passes through (-2, 3) and there are infinitely many such lines.
What is the equation of the line which passes through the point 2 3 and (What is the equation of the line that passes through (4, -1) and (-2, 3)? We have to find the equation of the line. Therefore, the equation of the line is 2x + 3y - 5 = 0.
What is the equation of straight line which is passes through the point 2 3 and equally intercept on both axes?Thus, the equation of line cuts off equal intercepts on the coordinate axes and passes through the point ( 2 , 3 ) is x + y = 5 .
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