Question

Please explain how to make an equation for a slope with only 2 plotted points.

For example: (-2,1) and (-3,-3)

I know the slope is 4, but what would you do to write it as an equation?

Answer 1

Step-by-step explanation:

I know you already know the slope, but I'll explain every step including finding the slope.

You are given two points, and you are asked to find the equation of the line that passes through the two points.

The equation of the line is

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

where (x1, y1) is a point on the line, and m is the slope.

The equation above is called the point-slope equation.

In your case, the points are (-2, 1) and (-3, -3). Let's find the slope.

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

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

We now have the slope, m = 4. Of course, you already knew this.

Now we use one of the points and the point-slope equation.

Let's use the point (-2, 1) and m = 4.

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

$y - 1 = 4[x - (-2)]$

$y - 1 = 4(x + 2)$

$y - 1 = 4x + 8$

$y = 4x + 9$   in slope-intercept form

$4x - y = -9$   in standard form