Answer:
y = -⅓x + 1.
y = -⅓ - 1
Step-by-step explanation:
The equation of the line shown can be expressed in slope-intercept form as [tex] y = mx + b [/tex].
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 = [tex] {y_2 - y_1}{x_2 - x_1} = \frac{0 - 1}{3 - 0} = \frac{-1}{3} = -\frac{1}{3} [/tex].
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
