Question

A line is defined by the equation y = two-thirds x minus 6. The line passes through a point whose y-coordinate is 0. What is the x-coordinate of this point?

A coordinate plane.

Answer 1

To find the x-coordinate of the point where the line intersects the y-axis (where the y-coordinate is 0), we can set \(y = 0\) in the equation of the line and solve for \(x\).

The line is given by the equation:

\[
y = \frac{2}{3}x - 6
\]

Setting \(y = 0\):

\[
0 = \frac{2}{3}x - 6
\]

Now, add 6 to both sides:

\[
6 = \frac{2}{3}x
\]

Next, to isolate \(x\), multiply both sides by the reciprocal of \(\frac{2}{3}\), which is \(\frac{3}{2}\):

\[
x = 6 \cdot \frac{3}{2}
\]

Calculating that gives:

\[
x = 9
\]

Therefore, the x-coordinate of the point where the line crosses the y-axis, and the y-coordinate is 0, is

\[
\boxed{9}
\]