Question

Please help me with a geometry problem, I don't understand.

Answer 1

The slope-intercept form:

$y=mx+b\\\\m=\dfrac{y_2-y_1}{x_2-x_1}$

m - slope

b - y-intercept

We have the points (1, -5) and (9, 11). Substitute:

$m=\dfrac{11-(-5)}{9-1}=\dfrac{16}{8}=2$

Therefore we have

$y=2x+b$

Put the coordinates of the point (1, -5) to the equation:

$-5=2(1)+b\\\\-5=2+b\qquad\text{subtract 2 from both sides}\\\\-7=b\to b=-7$

Answer: y = 2x - 7