Question

A line passes through the point (-7, 5) and has a slope of 1/2. Which is another point that the passes through?

A. (9, 13)
B. (-13, 9)
C. (13, 9)
D. (-9, 12)

Answer 1

To find another point that the line passes through, we can use the point-slope form of a line's equation, which is given by:

\[
y - y_1 = m(x - x_1)
\]

where \((x_1, y_1)\) is a point on the line and \(m\) is the slope. Given the point (-7, 5) and the slope \(m = \frac{1}{2}\), we can plug in the values:

\[
y - 5 = \frac{1}{2}(x + 7)
\]

Now, we can rewrite this equation in slope-intercept form (y = mx + b) or simply calculate a few values to determine if any of the provided multiple-choice answers lie on the line.

First, let's find the y-coordinate when \(x = 9\):

\[
y - 5 = \frac{1}{2}(9 + 7)
\]
\[
y - 5 = \frac{1}{2} \cdot 16
\]
\[
y - 5 = 8
\]
\[
y = 13
\]

So the point (9, 13) is on the line.

Now, we can check the other options too, if necessary:

For B. (-13, 9):
\[
y - 5 = \frac{1}{2}(-13 + 7)
\]
\[
y - 5 = \frac{1}{2}(-6)
\]
\[
y - 5 = -3 \Rightarrow y = 2 \quad (\text{not a solution})
\]

For C. (13, 9):
\[
y - 5 = \frac{1}{2}(13 + 7)
\]
\[
y - 5 = \frac{1}{2} \cdot 20
\]
\[
y - 5 = 10 \Rightarrow y = 15 \quad (\text{not a solution})
\]

For D. (-9, 12):
\[
y - 5 = \frac{1}{2}(-9 + 7)
\]
\[
y - 5 = \frac{1}{2}(-2)
\]
\[
y - 5 = -1 \Rightarrow y = 4 \quad (\text{not a solution})
\]

Thus, the only point that the line passes through is:

**A. (9, 13)**.