Question

What is the equation of the line that passes through `(1, 5)` and `(-2, 14)` in slope-intercept form?

Answer 1

`y = -3x + 8`

Explanation:

First, in order to solve this, we need to understand slope using two points. To put this simply in mathematical terms: `(y_2-y_1)/(x_2-x_1)`.

Let us say that `(-2, 14)` will be our `x_2, y_2` and `(1, 5)` as our `x_1, y_1`.

Plugging these variables into the slope formula shown previously: `(14-5)/(-2-1) = 9/-3 = -3`.

So we find that -3 is our slope, so using `y = mx + b`, we will replace `m` with `-3`, so it'll become `y = -3x + b`.

In order to solve for b, we will use either two points given to us in the question. Let's use `(-2, 14)`. So the point tells us that our x will equal -2 and our y will equal 14.

Thus: `14 = -3(-2) + b`.

Running through the calculation and we get `14 = 6 + b`.

Solving for b by subtracting 6 from both sides, we get `8 = b`.

So our slope-intercept form will be `y = -3x + 8`