Can you please provide the lines we need to work on?
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Recall that in order to find the equation of a line, we need at least TWO points on the plane. So we are going to use the two points that are marked with blue dots:
the oe more towards the left and down is the point (-3, -3) and the point to the right of the y-axis is (1, -1).
So we use them in the formula for the slope:
slope = (y2 - y1) / (x2 - x1)
in our case:
slope = (-3 - (-1)) / (-3 -1) = (-3+1) / (-4) = -2 / (-4) = 1/2
Then 1/2 is our slope.
So we use this slope "m" = 1/2 in the general slope-intercept form of a line:
y = m x + b
and replace m with "1/2":
y = (1/2) x + b
all we need now is the value of "b" (called the y-intercept), and for that we use either point in the equation above, for example point (1, -1), to determine its value:
-1 = (1/2) (1) + b
-1 = (1/2) + b
subtract 1/2 from both sides to isolate "b"
- 1 - 1/2 = b
then b = - 3/2
and now we can write the equation of this line in slope intercept formas:
y = (1/2) x - 3/2