a line passes through the points (-2, -4) and (4, 6). write its equation in slope - intercept form. write…

Answer:

$y=\frac{5}{3}x-\frac{2}{3}$

Explanation:

Step1: Calculate the slope

$m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{6-(-4)}{4-(-2)}=\frac{10}{6}=\frac{5}{3}$

Step2: Use point - slope form

$y - y_1=m(x - x_1)$, using the point $(-2,-4)$: $y+4=\frac{5}{3}(x + 2)$

Step3: Convert to slope - intercept form

$y+4=\frac{5}{3}x+\frac{10}{3}$, then $y=\frac{5}{3}x+\frac{10}{3}-4=\frac{5}{3}x+\frac{10 - 12}{3}=\frac{5}{3}x-\frac{2}{3}$