Question

Write a in slope-intercept form of the line that passes threw (-9,5) and (-3,3)

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 is the slope of the line

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

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

We have the following points:

$(x_ {1}, y_ {1}): (- 9,5)\\(x_ {2}, y_ {2}): (- 3,3)$

Substituting we have:

$m = \frac {3-5} {- 3 - (- 9)}\\m = \frac {-2} {- 3 + 9}\\m = \frac {-2} {6}\\m = - \frac {1} {3}$

Thus, the equation is of the form:

$y = - \frac {1} {3} x + b$

We substitute one of the points and find "b":

$3 = - \frac {1} {3} (- 3) + b\\3 = 1 + b\\3-1 = b\\b = 2$

Finally, the equation is of the form:

$y = - \frac {1} {3} x + 2$

Answer:

$y = - \frac {1} {3} x + 2$