Question

Select the equation that is parallel to 2y=4x+3

a
y=(1/2)x+4

b
y=2x-10

c
y=-2x-12

d
y=(-1/2)x-1

Answer 1

To determine which equation is parallel to \(2y = 4x + 3\), we first need to find the slope of the original equation.

1. Rewrite the given equation in slope-intercept form (y = mx + b):
\[
2y = 4x + 3
\]
Divide both sides by 2:
\[
y = 2x + \frac{3}{2}
\]

The slope (m) of this line is 2.

2. For two lines to be parallel, they must have the same slope.

Now, we will check the slopes of the given options:

a. \(y = \frac{1}{2}x + 4\) → slope = \(\frac{1}{2}\)

b. \(y = 2x - 10\) → slope = \(2\)

c. \(y = -2x - 12\) → slope = \(-2\)

d. \(y = -\frac{1}{2}x - 1\) → slope = \(-\frac{1}{2}\)

Only option **b** has the same slope (2) as the original equation, which means it is parallel.

Therefore, the answer is **b**: \(y = 2x - 10\).