For this case we have:
By definition, the slope-intercept equation of a line is given by:
[tex]y = mx + b[/tex]
Where [tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex] is the slope
b is the cut point with the y axis.
To find the slope we must have two points that go through the graph, observing the graph we have:
[tex](x_ {1} -y_ {1}) = (- 4,2)\\(x_ {2} -y_ {2}) = (4,4)[/tex]
Substituting we have:
[tex]m = \frac {4-2} {4 - (- 4)}[/tex]
[tex]m = \frac {4-2} {4 + 4}[/tex]
[tex]m = \frac {2} {8}[/tex]
[tex]m = \frac {1} {4}[/tex]
Then the slope-intercept equation is given by:[tex]y = \frac {1} {4} x + b[/tex]
To find the cut point with the "y" axis, we substitute any point:
[tex]4 = \frac {1} {4} 4 + b\\4 = 1 + b\\b = 4-1\\b = 3[/tex]
Finally the slope-intercept equation is given by: [tex]y = \frac {1} {4} x + 3[/tex]
answer:
[tex]y = \frac {1} {4} x + 3[/tex]
