Determine the equation of the line perpendicular to the line 4x+2y-7=0 that has the same x-intercept as the line 2x+3y-12=0

Let’s first make a blank equation in slope-intercept form: y=mx+b

To find the slope, we find the perpendicular slope to 4x+2y-7=0. First, change this to slope-intercept form:

4x+2y=7
2y=7-4x
y=-2x+(7/2)

The slope of this line is -2, so the perpendicular slope will be the opposite inverse, or 1/2. This is the first component.

Second, to find the x-intercept of 2x+3y-12=0, we have to set y=0 and solve:

2x+3(0)=12
2x=12
x=6 or (6,0)

So in total, we need a line with a slope of 1/2 passing through (6,0). Plug this back into y=mx+b:

0=1/2(6)+b
0=3+b
b=-3

So in total, the equation is y=(1/2)x-3.