Question

what are the equations of lines m and q? the equation of line m is (use integers or fractions for any numbers in the equation.)

Explanation:

Step1: Find slope of line m

Use slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$ with points $(1,-1)$ and $(4,4)$.
$m=\frac{4-(-1)}{4 - 1}=\frac{5}{3}$

Step2: Use point - slope form

Point - slope form is $y - y_1=m(x - x_1)$. Using point $(4,4)$ and $m = \frac{5}{3}$, we have $y - 4=\frac{5}{3}(x - 4)$.

Step3: Convert to slope - intercept form

$y-4=\frac{5}{3}x-\frac{20}{3}$
$y=\frac{5}{3}x-\frac{20}{3}+4$
$y=\frac{5}{3}x-\frac{20}{3}+\frac{12}{3}$
$y=\frac{5}{3}x-\frac{8}{3}$

Since lines m and q are perpendicular, the slope of line q is the negative reciprocal of the slope of line m. So slope of line q is $-\frac{3}{5}$. Using point $(2,6)$ and point - slope form $y - y_1=m(x - x_1)$:
$y - 6=-\frac{3}{5}(x - 2)$
$y-6=-\frac{3}{5}x+\frac{6}{5}$
$y=-\frac{3}{5}x+\frac{6}{5}+6$
$y=-\frac{3}{5}x+\frac{6}{5}+\frac{30}{5}$
$y=-\frac{3}{5}x+\frac{36}{5}$

Answer:

The equation of line m is $y=\frac{5}{3}x-\frac{8}{3}$, the equation of line q is $y =-\frac{3}{5}x+\frac{36}{5}$