Question

Write the equation of the line shown in point-slope form

Answer 1

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

$y-y_ {0} = m (x-x_ {0})$

Where:

m: Is the slope

$(x_ {0}, y_ {0}):$ It is a point through which the line passes

According to the data of the statement we have two points through which the line passes:

$(x_ {1}, y_ {1}): (-4,3)\\(x_ {2}, y_ {2}): (-3, -1)$

We found the slope:

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

Thus, the equation is of the form:

$y-y_ {0} = - 4 (x-x_ {0})$

We substitute one of the points:

$y-3 = -4 (x - (- 4))\\y-3 = -4 (x + 4)$

Finally, the equation is:

$y-3 = -4 (x + 4)$

Answer:

$y-3 = -4 (x + 4)$