Question
A line that includes the points \( (0,6) \) and \( (g, 5) \) has a slope of \( \frac{1}{4} \). What is the value of \( g \) ? \( g= \)
Ask by Matthews Ramos. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( g = -4 \)
Solution
To find the value of \( g \) for the line passing through the points \( (0, 6) \) and \( (g, 5) \) with a slope of \( \frac{1}{4} \), we can use the formula for the slope between two points:
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]
Plugging in the given points and slope:
\[
\frac{1}{4} = \frac{5 - 6}{g - 0} = \frac{-1}{g}
\]
Now, solve for \( g \):
\[
\frac{-1}{g} = \frac{1}{4} \implies g = -4
\]
**Answer:**
\( g = -4 \)
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Simplify this solution Bonus Knowledge
To find the value of \( g \), we can use the formula for the slope of a line, which is given by the change in \( y \) divided by the change in \( x \): \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \] For the points \( (0, 6) \) and \( (g, 5) \), we can let \( (x_1, y_1) = (0, 6) \) and \( (x_2, y_2) = (g, 5) \). Plugging the values into the slope formula, we get: \[ \frac{5 - 6}{g - 0} = \frac{1}{4} \] This simplifies to: \[ \frac{-1}{g} = \frac{1}{4} \] To eliminate the fraction, we can cross-multiply: \[ -1 \cdot 4 = 1 \cdot g \] This simplifies to: \[ -4 = g \] Thus, the value of \( g \) is: \[ g = -4 \]
