What is the equation in slope-intercept form of the line that passes through the points (5,3) and (–1,6)

Answer 1

Start with two-point form:

(y - 3) / (x - 5) = (6 - 3) / (-1 -5)

Can you simplify and convert to slope-intercept form?

Answer 2

So we need to create an equation in the form of y=mx+b. Remember, m is the slope and b is the y-intercept.

1) START BY FINDING THE SLOPE.

The equation to find the slope is m = rise / run. In other words, it is m = difference in y values / difference in x values.

In this case m = (3 - 6) / (5 - -1) = -3 / 6 = -0.5

2) FIND THE Y-INTERCEPT

Now go back to the equation we are trying to make. Use one of the points we already know as the x and y values, then solve for b. We will use (5,3) as an example.

y = mx + b

3 = (-0.5)(5) + b

3 = -2.5 + b

5.5 = b

3) PUT IT ALL TOGETHER!

Now we know m and b, so we have a full equation. Our equation is y = -0.5x + 5.5

4) CHECK YOUR WORK

Always check your work quickly to make sure you didn’t make a mistake. Let’s use our other point, (-1,6) to make sure our equation is correct. To do this, let’s plug in -1 as our x value and see if we get 6 as our answer.

y = -0.5(-1) + 5.5 = 0.5 + 5.5 = 6

We got a y value of 6 when we used an x value of -1 so we know our equation is correct!