Question
A line with a slope of
–
3
2
passes through the points (g,
–
4) and (3,
–
7). What is the value of g?
–
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:
\[
\boxed{2}
\]
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
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:
\[
\boxed{2}
\]
There are no human answers yet. A form for humans to post answers is coming very soon!