Question

Write an equation in standard form for each line.

Answer 1

The standard form: Ax + By = C.

The point-slope form:

$y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}$

7. We have the points (4, -7) and (2, -3). Substitute:

$m=\dfrac{-3-(-7)}{2-4}=\dfrac{4}{-2}=-2\\\\y-(-7)=-2(x-4)\qquad|\text{use distributive property}\\\\y+7=(-2)(x)+(-2)(-4)\\\\y+7=-2x+8\qquad|-7\\\\y=-2x+1\qquad|+2x\\\\\boxed{2x+y=1}$

8. We have the points (1, 5) and (-10, -6). Substitute:

$m=\dfrac{-6-5}{-10-1}=\dfrac{-11}{-11}=1\\\\y-5=1(x-1)\\\\y-5=x-1\qquad|+5\\\\y=x+4\qquad|-x\\\\-x+y=4\qquad|\text{change the signs}\\\\\boxed{x-y=-4}$