Question

Write the slope intercept form equation from the graph.

Answer 1

For this case we have that by definition, the equation of a line in the slope-intersection form is given by:

$y = mx + b$

Where:

m: It's the slope

b: It is the cut-off point with the y axis

According to the image, the line goes through the following points:

$(x_ {1}, y_ {1}): (2,1)\\(x_ {2}, y_ {2}): (0,4)$

So, the slope is:

$m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {4-1} {0-2} = \frac {3} {- 2} = - \frac {3} {2}$

Thus, the equation is of the form:

$y = - \frac {3} {2} x + b$

We substitute a point and find "b":

$4 = -\frac {3} {2} (0) + b\\4 = b$

Finally, the equation is:

$y = - \frac {3} {2} x + 4$

Answer:

$y = - \frac {3} {2} x + 4$