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=(1)/(3)x-(2)/(3)\to m=(1)/(3)`

Therefore searched line equation is:

`y=(1)/(3)x+b`

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

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

Answer:
`y=(1)/(3)x+3`