Question

Which equation has a slope of 1/2 and a y-intercept of -5?
x-2y=10
2x-y=5
2x+y=-5
x+2y=-10

Answer 1

To find the equation with a slope of \( \frac{1}{2} \) and a y-intercept of -5, we can use the slope-intercept form of a linear equation, which is given by:

\[
y = mx + b
\]

where \( m \) is the slope and \( b \) is the y-intercept. Thus, substituting \( m = \frac{1}{2} \) and \( b = -5 \), we can write:

\[
y = \frac{1}{2}x - 5
\]

Now, we will check which of the given equations is equivalent to this:

1. **Equation: \( x - 2y = 10 \)**

Rearranging:

\[
-2y = -x + 10 \quad \Rightarrow \quad y = \frac{1}{2}x - 5
\]
This matches our desired equation.

2. **Equation: \( 2x - y = 5 \)**

Rearranging:

\[
-y = -2x + 5 \quad \Rightarrow \quad y = 2x - 5
\]
This has a slope of 2.

3. **Equation: \( 2x + y = -5 \)**

Rearranging:

\[
y = -2x - 5
\]
This has a slope of -2.

4. **Equation: \( x + 2y = -10 \)**

Rearranging:

\[
2y = -x - 10 \quad \Rightarrow \quad y = -\frac{1}{2}x - 5
\]
This has a slope of -\(\frac{1}{2}\).

Among the equations we analyzed, the first equation \( x - 2y = 10 \) is the only one that has a slope of \( \frac{1}{2} \) and a y-intercept of -5.

Therefore, the answer is:

**\( x - 2y = 10 \)**.