Get the equation of the line containing PQ using the point-slope formula:
<em>y</em> - (-2) = 3/2 (<em>x</em> - (-6))
Solve for <em>y</em> to get it in slope-intercept form:
<em>y</em> = 3/2 <em>x</em> + 7
so the <em>y</em>-intercept is (0, 7).
The line containing QR is then
<em>y</em> - 7 = -3/4 (<em>x</em> - 0)
or
<em>y</em> = -3/4 <em>x</em> + 7
The point R is on the <em>x</em>-axis, so its <em>y</em>-coordinate is 0. Plug in <em>y</em> = 0 and solve for <em>x</em> to get the other coordinate:
0 = -3/4 <em>x</em> + 7
3/4 <em>x</em> = 7
<em>x</em> = 4/3×7 = 28/3
So the point R has coordinates (28/3, 0).
