Question

HELP WITH THIS GRAPH?

Answer 1

For this case we have:

By definition, the slope-intercept equation of a line is given by:

$y = mx + b$

Where $m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}$ 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:

$(x_ {1} -y_ {1}) = (- 4,2)\\(x_ {2} -y_ {2}) = (4,4)$

Substituting we have:

$m = \frac {4-2} {4 - (- 4)}$

$m = \frac {4-2} {4 + 4}$

$m = \frac {2} {8}$

$m = \frac {1} {4}$

Then the slope-intercept equation is given by:$y = \frac {1} {4} x + b$

To find the cut point with the "y" axis, we substitute any point:

$4 = \frac {1} {4} 4 + b\\4 = 1 + b\\b = 4-1\\b = 3$

Finally the slope-intercept equation is given by: $y = \frac {1} {4} x + 3$

answer:

$y = \frac {1} {4} x + 3$