When lines are parallel, they have the same slope.
- x+2y=12
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 information, we can more easily identify the slope m and y-intercept b.
y=1/2x+ 6
This means we can write a general equation in slope-intercept form for all lines parallel to the given equation.
y=1/2x+ b
We are asked to write the equation of a line parallel to the given equation that passes through the given point ( 4, 0). 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.
Now that we have the y-intercept, we can conclude that the line given by the following equation is parallel to - x+2y=12 and passes through (4,0).
y=1/2x+( - 2) ⇔ y=1/2x-2
Finally, we can verify our answer by graphing both lines on the same coordinate plane. If they are parallel, they will never intersect.
We can see by looking at the graphs of the functions that they are indeed parallel.
