Question

Write the point-slope form of the equation of the line that passes through the points (-3, 5) and (-1, 4). Please answer quickly I need it in five minutes!

Answer 1

The point-slope form of the equation of a line is

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

where

$(x_1, y_1)$

is a point on the line, and

$m$

is the slope of the line.

We can use either one of the two given points as the point on the line.
We also need to find the slope. We can use the coordinates of the two given points to find the slope of the line.

The slope of the line that passes through points

$(x_1, y_1)$ and $(x_2, y_2)$

is

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

Let's find the slope using (-3, 5) as point 1 and (-1, 4) as point 2.

$m = \dfrac{4 - 5}{-1 - (-3)} = \dfrac{-1}{-1 + 3} = \dfrac{-1}{2} = -\dfrac{1}{2}$

Now we use the point-slope formula with point 1 and the slope we found just above.

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

$y - 5 = -\dfrac{1}{2}(x - (-3))$