Question

If a point on the line y=−
4
3
​
x+7 has a y-coordinate of 1, what is its x-coordinate?

x=8

x=1

x=13

x=−20

Answer 1

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 \( x \):

1. Subtract 7 from both sides:

\[
1 - 7 = -\frac{4}{3}x
\]
\[
-6 = -\frac{4}{3}x
\]

2. Multiply both sides by -1:

\[
6 = \frac{4}{3}x
\]

3. To isolate \( x \), multiply both sides by the reciprocal of \( \frac{4}{3} \) which is \( \frac{3}{4} \):

\[
x = 6 \cdot \frac{3}{4}
\]

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.