Question

Lines p, q, and r all pass through point (-3,4). Line p has slope 4 and is perpendicular to line q. Line r passes through Quadrants 1 and Quadrants 2 only. Write an equation for each line. Then graph the three lines on the same coordinate plane.

Answer 1

Answer:

Part 1) The equation of line p is $y=4x+16$

Part 2) The equation of line q is $y=-\frac{1}{4}x+\frac{13}{4}$

Part 3) The equation of line r is $y=4$

The graph in the attached figure

Step-by-step explanation:

step 1

Find the equation of the line p

we have

$m=4\\point\ (-3,4)$

Find the equation in point slope form

$y-y1=m(x-x1)$

substitute

$y-4=4(x+3)$ ----> equation in point slope form

Convert to slope intercept form

$y-4=4x+12$

$y=4x+12+4$

$y=4x+16$

step 2

Find the equation of line q

we know that

If two lines are perpendicular, then their slope are opposite reciprocal (the product of their slopes is equal to -1)

we have that

Line q is perpendicular to line q

so

$m_q*m_p=-1$

we have

$m_p=4$

therefore

$m_q=-\frac{1}{4}$

we have

$m=-\frac{1}{4}\\point\ (-3,4)$

Find the equation in point slope form

$y-y1=m(x-x1)$

substitute

$y-4=-\frac{1}{4}(x+3)$ ----> equation in point slope form

Convert to slope intercept form

$y-4=-\frac{1}{4}x-\frac{3}{4}$

$y=-\frac{1}{4}x-\frac{3}{4}+4$

$y=-\frac{1}{4}x+\frac{13}{4}$

step 3

Find the equation of line r

we know that

Line r passes through Quadrants 1 and Quadrants 2 only and passes through the point (-3,4)

therefore

The equation of Line r must be equal to the y-coordinate of the given point

$y=4$ ----> is a horizontal line

step 4

Graph the three lines

using a graphing tool

see the attached figure