Question

Enter the equation of the line in slope-intercept form.

Answer 1

Given:

The line parallel to y = −x that passes through (7, 2.5).

To find:

The slope intercept form of the given line.

Solution:

Slope intercept form of the line is

$y=mx+b$

where, m is slope and b is y-intercept.

On comparing y = −x with slope intercept form, we get

$m=-1$

So, slope of y=-x is -1.

Slope of parallel lines are same. Thus, slope of required line is -1.

Required line passes through (7,2.5) with slope -1. So, the equation of line is

$y-y_1=m(x-x_1)$

$y-2.5=-1(x-7)$

$y-2.5=-x+7$

Add 2.5 on both sides.

$y-2.5+2.5=-x+7+2.5$

$y=-x+9.5$

Therefore, the equation of the line that passes through (7, 2.5) is $y=-x+9.5$.