Question

Write an equation for the line in slope intercept form to parallel to -x + 3y =-2 that contains the point (12,7)

Answer 1

The parallel lines have the same slope.

The slope-intercept form:

$y=mx+b$

m - slope

b - y-intercept

We have

$-x+3y=-2\qquad|\text{add x to both sides}\\\\3y=x-2\qquad|\text{divide both sides by 3}\\\\y=\dfrac{1}{3}x-\dfrac{2}{3}\to m=\dfrac{1}{3}$

Therefore searched line equation is:

$y=\dfrac{1}{3}x+b$

The line passes through point (12, 7). Put the coordinates of the point into the equation of the line:

$7=\dfrac{1}{3}(12)+b\\\\7=4+b\qquad|\text{subtract 4 from both sides}\\\\3=b\to b=3$

Answer: $y=\dfrac{1}{3}x+3$