Question

A line with a slope of

3
2
passes through the points (g,

4) and (3,

7). What is the value of g?

Answers

Answered by GPT-4o mini
To find the value of \( g \) given that the line has a slope of \( -\frac{3}{2} \) and passes through the points \( (g, -4) \) and \( (3, -7) \), we can use the slope formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Here, \( (x_1, y_1) = (g, -4) \) and \( (x_2, y_2) = (3, -7) \). Plugging into the slope formula, we have:

\[
-\frac{3}{2} = \frac{-7 - (-4)}{3 - g}
\]

Simplifying the numerator:

\[
-\frac{3}{2} = \frac{-7 + 4}{3 - g}
\]
\[
-\frac{3}{2} = \frac{-3}{3 - g}
\]

Now we can cross-multiply to eliminate the fraction:

\[
-3(3 - g) = -\frac{3}{2}(2)
\]
\[
-3(3 - g) = -3
\]

Dividing both sides by -3 gives:

\[
3 - g = 1
\]

Now, we solve for \( g \):

\[
g = 3 - 1
\]
\[
g = 2
\]

Thus, the value of \( g \) is:

\[
\boxed{2}
\]
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