Question

Complete the point slope equation of the line through (-5, 7) and (-4, 0).​

Answer 1

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

$y = mx + b$

Where:

m: It's the slope

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

We have two points:

$(x_ {1}, y_ {1}): (- 5,7)\\(x_ {2}, y_ {2}): (- 4,0)$

We found the slope:

$m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {0-7} {- 4 - (- 5)} = \frac {-7} {-4 + 5} = \frac {-7} {1} = - 7$

Thus, the equation is of the form:

$y = -7x + b$

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

$0 = -7 (-4) + b\\0 = 28 + b\\b = -28$

Finally, the equation is:

$y = -7x-28$

Answer:

$y = -7x-28$