Question

Explain how to write an equation for the line that contains the point (2, -3) and is perpendicular to the
graph of x + 2y = 2

Answer 1

Answer:

$y=2x-7$

Step-by-step explanation:

Convert to slope-intercept form

$x+2y=2\\\\2y=2-x\\\\y=1-\frac{1}{2}x\\ \\y=-\frac{1}{2}x+1$

Find the opposite reciprocal slope

Original --> $-\frac{1}{2}$

Opposite Sign --> $\frac{1}{2}$

Reciprocal --> $2$

Find the new y-intercept given the point (2,-3)

$y=2x+b\\\\-3=2(2)+b\\\\-3=4+b\\\\b=-7$

Final Equation

$y=2x-7$