To find the x-coordinate of a point on the line given by the equation \( y = -\frac{4}{3}x + 7 \) with a y-coordinate of 1, we substitute \( y = 1 \) into the equation:
\[ 1 = -\frac{4}{3}x + 7 \]
Next, we can rearrange the equation to solve for \( x \):
- Subtract 7 from both sides:
\[ 1 - 7 = -\frac{4}{3}x \] \[ -6 = -\frac{4}{3}x \]
- Multiply both sides by -1:
\[ 6 = \frac{4}{3}x \]
- To isolate \( x \), multiply both sides by the reciprocal of \( \frac{4}{3} \) which is \( \frac{3}{4} \):
\[ x = 6 \cdot \frac{3}{4} \]
- Calculate \( 6 \cdot \frac{3}{4} \):
\[ x = \frac{18}{4} = \frac{9}{2} = 4.5 \]
Looking at the options provided (8, 1, 13, -20), \( x = 4.5 \) is not listed among them, indicating that none of the options are correct.
Let's double-check: The original equation \( y = -\frac{4}{3}x + 7 \) when \( y = 1 \) indeed leads us to \( x = 4.5 \).
So it appears that the correct answer is \( x = 4.5 \), which was not in the provided options.