Question

Complete the equation of the line through (-9,-9) and (-6,0)

Answer 1

For this case we have that by definition, the equation of the line of 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.

According to the data of the statement we have the following points:

$(x_ {1}, y_ {1}): (- 9, -9)\\(x_ {2}, y_ {2}): (- 6,0)$

We found the slope:

$m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {0 - (- 9)} {- 6 - (- 9)} = \frac { 9} {- 6 + 9} = \frac {9} {3} = 3$

Thus, the equation is of the form:

$y = 3x + b$

We substitute one of the points and find b:

$0 = 3 (-6) + b\\0 = -18 + b\\b = 18$

Finally, the equation is:

$y = 3x + 18$

Answer:

$y = 3x + 18$