Question

Which equation has a slope of -4 and a y-intercept at 2?

x+2y=4
4x+y=2
4x-y=-2
x-3y=-8

Answer 1

To find the equation that has a slope of -4 and a y-intercept of 2, we can start with the slope-intercept form of a linear equation, which is:

\[ y = mx + b \]

where \( m \) is the slope and \( b \) is the y-intercept. Given that the slope \( m = -4 \) and the y-intercept \( b = 2 \), we can write the equation as:

\[ y = -4x + 2 \]

Now, we need to find an equivalent equation among the options provided:

1. **For \( x + 2y = 4 \)**:
\[
2y = -x + 4 \quad \Rightarrow \quad y = -\frac{1}{2}x + 2
\]
(Slope is \(-\frac{1}{2}\))

2. **For \( 4x + y = 2 \)**:
\[
y = -4x + 2
\]
(Slope is \(-4\))

3. **For \( 4x - y = -2 \)**:
\[
-y = -4x - 2 \quad \Rightarrow \quad y = 4x + 2
\]
(Slope is \(4\))

4. **For \( x - 3y = -8 \)**:
\[
-3y = -x - 8 \quad \Rightarrow \quad y = \frac{1}{3}x + \frac{8}{3}
\]
(Slope is \(\frac{1}{3}\))

The equation \( 4x + y = 2 \) simplifies to \( y = -4x + 2 \), which has a slope of -4 and a y-intercept of 2.

So, the correct answer is:

**4x + y = 2**.