Which of the following lines is parallel to the line y = (-1/4) x+5?

y=4x+7

y=-4x-5

y = (-1/4) x-3

Answer: y = (-1/4) x - 3

Step-by-step explanation:

Which of the following lines is parallel to the line y = (-1/4) x+5

Two lines are parallel to each other if they have the same slope,

Slope of line 1 = slope of line 2

Looking at y = (-1/4) x+5,

we will compare it with the slope-intercept equation, y = mx+c

Slope of y = (-1/4) x+5 = - 1/4

Now let's examine the options to see the one such that has the same value with our slope, - 1/4

1) y=4x+7

From this equation, slope = 4

4 * - 1/4 = - 1

This means lines (-1/4) x+5 and y=4x+7 are not parallel to each other since their slopes are unequal

2) y=-4x-5, slope = - 4

This means lines (-1/4) x+5 and y=4x-5 are not parallel to each other since their slopes are unequal.

3) y = (-1/4) x-3

slope = - 1/4

This means lines (-1/4) x+5 and y = (-1/4) x-3 are parallel to each other since their slopes are equal. This means equations y = (-1/4) x-3 and y = (-1/4) x+5

are parallel.

In conclusion, line y = (-1/4) x-3 is parallel to y = (-1/4) x+5