Question

Select the equation that is parallel to y=4x-10 and has a y intercept of 1

a
y=(-1/4)x+1

b
y=4x+1

c
y=-4x+1

Answer 1

To determine which equation is parallel to \( y = 4x - 10 \) and has a y-intercept of 1, we need to recall that parallel lines have the same slope.

The slope of the given line \( y = 4x - 10 \) is 4. Therefore, the equation of a line that is parallel to it will also have a slope of 4.

Next, we need to find the equation that has the y-intercept of 1. The general form of the equation for a line with slope \( m \) and y-intercept \( b \) is:

\[
y = mx + b
\]

Substituting the parallel line's slope and the desired y-intercept, we get:

\[
y = 4x + 1
\]

Now, let's check the options:

- a) \( y = (-1/4)x + 1 \) (This has a slope of -1/4, not parallel)
- b) \( y = 4x + 1 \) (This has a slope of 4, which is parallel)
- c) \( y = -4x + 1 \) (This has a slope of -4, not parallel)

The correct choice is:
**b) \( y = 4x + 1 \)**