What is an equation of the line that passes through the points (-8, 3)and (-2, 0)

Question

What is an equation of the line that passes through the points

Answer 1

Hi, Ando!

In order to write the equation of a line in y = mx + b form, there are two things that we need: the slope of the line (m), and the y-intercept of the line (b). Let's start by solving for the slope, m.

The slope of a line is equal to the change in y over the change in x: m = Δy / Δx = (y₂ - y₁) / (x₂ - x₁)

We can plug the points that we have been given into this equation for slope.

Let (-8, 3) = (x₁, y₁)

Let (-2, 0) = (x₂, y₂)

m = (0 - 3) / (-2 - -8))

m = -3 / 6

m = -1/2

Now that we have our slope, we can substitute it into our general formula to obtain the following:

y = (-1/2)x + b

Finally, we can plug in either one of our points into this equation to solve for b. Let's choose (-2, 0) = (x, y).

y = (-1/2)x + b

0 = (-1/2)(-2) + b

0 = 1 + b

b = -1

Finally, we can plug in our m and b into our general equation to find our final answer:

y = (-1/2)x + (-1)

y = (-1/2)x - 1

I hope that this explanation was helpful, and please don't hesitate to reach out if you have any further questions!

Answer 2

Given the two points, you can first find the slope and use that in either the slope-intercept or point-slope forms of the line.

Slope (m) = rise/run = (y₂ - y₁)/(x₂ - x₁)

(0 - 3)/(-2 - (-8)) = -3/6 = -1/2

The point-slope form using (-8, 3) would be y - 3 = -1/2(x - (-8))

y - 3 = -1/2(x + 8) = -(1/2)x - 4

y = -(1/2)x - 1

Using the slope-intercept form (y = mx + b), can solve for the y-intercept (b): 3 = -(1/2)(-8) + b

3 = 4 + b → b = -1

so the equation is y = -(1/2)x - 1 again.

Check result using the Desmos Graphing Calculator website.