Question

Which line has an equation of y = negative 5 x + 4 in slope-intercept form?
a line passing through the points (1, 9) and (3, 19)
a line passing through the points (2, –14) and (4, –24)
a line passing through the points (1, 1) and (3, 11)
a line passing through the points (2, –6) and (4, –16)

Answer 1

To determine which given lines have the equation \( y = -5x + 4 \), we need to calculate the slope of each pair of points and see if it matches the slope of the given equation, which is -5.

1. **Line through (1, 9) and (3, 19):**
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{19 - 9}{3 - 1} = \frac{10}{2} = 5
\]
The slope is 5, which does not match -5.

2. **Line through (2, –14) and (4, –24):**
\[
\text{slope} = \frac{-24 - (-14)}{4 - 2} = \frac{-24 + 14}{2} = \frac{-10}{2} = -5
\]
The slope is -5, which matches.

3. **Line through (1, 1) and (3, 11):**
\[
\text{slope} = \frac{11 - 1}{3 - 1} = \frac{10}{2} = 5
\]
The slope is 5, which does not match -5.

4. **Line through (2, –6) and (4, –16):**
\[
\text{slope} = \frac{-16 - (-6)}{4 - 2} = \frac{-16 + 6}{2} = \frac{-10}{2} = -5
\]
The slope is -5, which matches.

Therefore, the correct answers are **the line passing through the points (2, –14) and (4, –24)** and **the line passing through the points (2, –6) and (4, –16)**. Both these lines have a slope of -5, which matches the given equation.