When lines are parallel, they have the same slope. To help us identify the slope of this line, let's first convert it into slope-intercept form, y= mx+ b, where m is the slope and (0, b) is the y-intercept.
With this, we can more easily identify the slope m and y-intercept b.
y= 1/3x- 4
Now that we have identified the slope, we can write a general equation in slope-intercept form for all lines parallel to the given equation.
y= 1/3x+ b
We are asked to write the equation of a line parallel to the given equation that passes through the given point ( 18, 2). By substituting this point into the general equation for x and y, we will be able to solve for the y-intercept b of the parallel line.
As we can see we got exactly the same y-intercept as in the given equation. So we can write the equation for the line that is parallel to 3y-x=-12 and passes through (18,2).
y= 1/3x- 4
