Question

Which equation represents the line that passes through the points (4, 6) and (−2, −1)?

Answer 1

Find the slope first by using rise/run

$m=\frac{6-(-1)}{4-(-2)}\\m=\frac{6+1}{4+2}\\m=\frac{7}{6}$

$y=mx+b\\y=\frac{7}{6}x+b$

We need to find the y-intercept. Substituting one of given ordered pairs. I will use (-2,-1).

Substitute x = -2 and y = -1 in the equation.

$-1=\frac{7}{6}(-2)+b\\-1=\frac{7}{-3}+b\\-1=-\frac{7}{3}+b\\-1+\frac{7}{3}=b\\b=\frac{4}{3}$

Thus the y-intercept is 4/3.

From y = mx+b, the equation is.

$y=\frac{7}{6}x+\frac{4}{3}$