Question

What is the equation of the line shown?

what is the equation of a parallel line with a y-intercept of -1?​

Answer 1

y = -⅓x + 1.

y = -⅓ - 1

Explanation:

The equation of the line shown can be expressed in slope-intercept form as
`y = mx + b`.

b = y-intercept, which is where the line intercepts the y-axis.

The line intercepts the y-axis at 1. Therefore b = 1.

m = slope = rise/run =
`{y_2 - y_1}{x_2 - x_1} = (0 - 1)/(3 - 0) = (-1)/(3) = -(1)/(3)`.

Substitute b = 1 and m = -⅓ into y = mx + b to get the equation of the line shown. Thus, the equation would be:

y = -⅓x + 1.

The equation of a line with y-intercept (b) of -1 that is parallel to the line shown, would have the same slope as the line shown but different y-intercept.

Thus, the slope of the line shown is m = -⅓, this would also be the slope of the line parallel to it.

Therefore, substitute m = -⅓ and b = -1 into y = mx + b.

y = -⅓x + (-1)

y = -⅓ - 1

The equation of the line with y-intercept big -1 that is parallel to the line shown on the graph, is y = -⅓ - 1