Question

Two points on a line are (-10, 1) and (5,-5). If

the y-coordinate of another point on the line is
-3, what is the x-coordinate?
​

Answer 1

The x-coordinate is 0

Explanation:

step 1

Find the slope m of the line

we have the points

(-10, 1) and (5,-5)

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

substitute the values

`m=(-5-1)/(5+10)`

`m=(-6)/(15)`

Simplify

`m=-(2)/(5)`

step 2

Find the equation of the line in slope intercept form

`y=mx+b`

where

m is the slope

b is the y-intercept

we have

`m=-(2)/(5)`

`point\ (-10,1)`

substitute in the equation and solve for b

`1=-(2)/(5)(-10)+b`

`1=4+b`

`b=1-4=-3`

The equation of the line is

`y=-(2)/(5)x-3`

step 3

Find the x-coordinate of another point in the line if the y-coordinate is -3

For y=-3

substitute in the equation and solve for x

`-3=-(2)/(5)x-3`

`-3+3=-(2)/(5)x`

`0=-(2)/(5)x`

`x=0`

The point is (0,-3) -----> the y-intercept

therefore

The x-coordinate is 0