Question

A line has a slope of
–
7
2
and includes the points (t,
–
10) and (
–
9,
–
3). What is the value of t?

Answer 1

To find the value of \( t \) for the line with a slope of \( -\frac{7}{2} \) that passes through the points \( (t, -10) \) and \( (-9, -3) \), we can use the slope formula:

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

We can denote the points as \( (x_1, y_1) = (t, -10) \) and \( (x_2, y_2) = (-9, -3) \).

Now substituting the coordinates into the slope formula:

\[
-\frac{7}{2} = \frac{-3 - (-10)}{-9 - t}
\]

Simplifying the numerator:

\[
-\frac{7}{2} = \frac{-3 + 10}{-9 - t} = \frac{7}{-9 - t}
\]

Now, we'll cross-multiply to eliminate the fraction:

\[
-7(-9 - t) = 2 \cdot 7
\]

This simplifies to:

\[
7(9 + t) = 14
\]

Expanding the left side:

\[
63 + 7t = 14
\]

Now, we'll isolate \( t \):

\[
7t = 14 - 63
\]
\[
7t = -49
\]
\[
t = -7
\]

Thus, the value of \( t \) is

\[
\boxed{-7}
\]