Question

Write the slope-intercept form of the equation of the line described.

Answer 1

                                                  7)

Given the line

$y=-x+2$

We know that the slope-intercept form of the line equation is

$y=mx+b$

here

m is the slope and b is the intercept

Thus, the slope = -1

We know that the parallel lines have the same. Thus, the slope of the parallel line is: -1

Using point-slope of the line equation

$y-y_1=m\left(x-x_1\right)$

substituting the values m = -1 and the point (4, 0)

$y-0 = -1 (x-4)$

Writing in the slope-intercept form

$y = -x+4$

Thus, the slope-intercept form of the equation of the line equation parallel to y=-x+ 2 will be:

• $y = -x+4$

                                                      8)

Note: Your line is a little bit unclear. But, I am assuming the

ine is: y = -x-1

Given the assumed line

y = -x-1

We know that the slope-intercept form of the line equation is

$y=mx+b$

here

m is the slope and b is the intercept

Thus, the slope = m = -1

We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:

slope = m = -1

perpendicular slope = – 1/m = -1/-1 = 1

Using point-slope of the line equation

$y-y_1=m\left(x-x_1\right)$

substituting the values m = 1 and the point (4, 3)

$y - 3 = 1 (x-4)$

Writing in the slope-intercept form

y-3 = x-4

y = x-4+3

y = x - 1

Thus, the slope-intercept form of the equation of the line equation perpendicular to y = -x-1 will be:

• y = x - 1