Question

Write the point slope form of the equation of the line passing through the points (-5, 6) and (0.1).

Answer 1

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

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

Where:

m: It's the slope

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

$m = \frac {y2-y1} {x2-x1}$

We have as data two points, replacing:

$m = \frac {1-6} {0 - (- 5)}\\m = \frac {1-6} {0 + 5}\\m = \frac {-5} {5}\\m = -1$

We substitute a point, then the equation is:

$(y-1) = - 1 (x-0)\\(y-1) = - x$

Answer:

$(y-1) = - x$

Answer 2

Answer: $y-6=-(x+5)$

Step-by-step explanation:

The Point-slope form of the equation of the line is:

$y-y_1=m(x-x_1)$

Where "m" is the slope of the line and $(x_1,y_1)$ is a point on the line.

We know that this line passing through the points (-5,6) and (0,1), then we can find the slope with this formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

Substituting, we get:

 $m=\frac{1-6}{0-(-5)}=-1$

Finally, we can substitute the point (-5,6) and the slope into  $y-y_1=m(x-x_1)$, then:

$y-6=-(x-(-5))$

$y-6=-(x+5)$