The equation of the line in the point-slope form is y - 15 =
(x - 10)
Step-by-step explanation:
The point-slope form of a linear equation is
, where
- m is the slope of the line, where
,
and
are two points on the line
is a point on the line
∵ Point A = (10 , 15)
∵ The x-coordinate of the second point is 125% of x-coordinate
of point A
∴ x-coordinate of second point =
× 10
∴ x-coordinate of second point = 12.5
∵ The y-coordinate of the second point is 75% of y-coordinate
of point A
∴ y-coordinate of second point =
× 15
∴ y-coordinate of second point = 11.25
∴ The coordinates of the second point are (12.5 , 11.25)
Let us find the slope of the line by using the rule of it above
∵
= (10 , 15)
∵
= (12.5 , 11.25)
∴ ![m=\frac{11.25-15}{12.5-10}=\frac{-3.75}{2.5}=-\frac{3}{2}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B11.25-15%7D%7B12.5-10%7D%3D%5Cfrac%7B-3.75%7D%7B2.5%7D%3D-%5Cfrac%7B3%7D%7B2%7D)
Now we can write the equation
∵ The point-slope form is ![y-y_{1}=m(x-x_{1})](https://tex.z-dn.net/?f=y-y_%7B1%7D%3Dm%28x-x_%7B1%7D%29)
∵ ![m=-\frac{3}{2}](https://tex.z-dn.net/?f=m%3D-%5Cfrac%7B3%7D%7B2%7D)
∵
= (10 , 15)
- Substitute these values in the form of the equation
∴ y - 15 =
(x - 10)
The equation of the line in the point-slope form is y - 15 =
(x - 10)
Learn more:
You can learn more about the linear equation in brainly.com/question/4152194
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