Question
A line that includes the points \( (-3, c) \) and \( (-2,2) \) has a slope of 10. What is the value of \( c \) ? \( c=\square \)
Ask by Rowe Moreno. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( c = -8 \)
Solution
To find the value of \( c \) such that the line passing through the points \( (-3, c) \) and \( (-2, 2) \) has a slope of 10, we can use the slope formula:
\[
\text{Slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]
Plugging in the given values:
\[
10 = \frac{2 - c}{-2 - (-3)}
\]
Simplify the denominator:
\[
10 = \frac{2 - c}{1}
\]
This simplifies to:
\[
10 = 2 - c
\]
Solving for \( c \):
\[
c = 2 - 10
\]
\[
c = -8
\]
**Answer:**
\(-8\)
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Simplify this solution Bonus Knowledge
To find the value of \( c \) in the line that includes the points \( (-3, c) \) and \( (-2, 2) \) with a slope of 10, we can use the formula for slope: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting our points and the slope: \[ 10 = \frac{2 - c}{-2 - (-3)} \] This simplifies to: \[ 10 = \frac{2 - c}{-2 + 3} = \frac{2 - c}{1} \] Thus, we have: \[ 10 = 2 - c \] Now, solving for \( c \): \[ c = 2 - 10 = -8 \] So, the value of \( c \) is \( -8 \).
