How To Find Slope Intercept Form With Two Points

An equation in the gradient-intercept form is written as

$$y=mx+b$$

Where m is the slope of the line and b is the y-intercept. You tin use this equation to write an equation if you know the gradient and the y-intercept.

Example

Observe the equation of the line

Choose ii points that are on the line

Calculate the slope between the ii points

$$thou=\frac{y_{2}\, -y_{1}}{x_{2}\, -x_{ane}}=\frac{\left (-1 \correct )-three}{3-\left ( -three \correct )}=\frac{-four}{vi}=\frac{-ii}{3}$$

We tin find the b-value, the y-intercept, by looking at the graph

b = ane

Nosotros've got a value for m and a value for b. This gives us the linear function

$$y=-\frac{2}{3}ten+1$$

In many cases the value of b is not as easily read. In those cases, or if you're uncertain whether the line really crosses the y-centrality in this particular bespeak you can calculate b past solving the equation for b and then substituting x and y with 1 of your two points.

We can utilize the case above to illustrate this. We've got the two points (-iii, 3) and (3, -1). From these ii points nosotros calculated the slope

$$m=-\frac{two}{three}$$

This gives u.s. the equation

$$y=-\frac{ii}{3}x+b$$

From this nosotros tin can solve the equation for b

$$b=y+\frac{two}{3}x$$

And if we put in the values from our beginning point (-3, 3) nosotros go

$$b=3+\frac{2}{3}\cdot \left ( -iii \correct )=3+\left ( -2 \correct )=1$$

If we put in this value for b in the equation we get

$$y=-\frac{two}{iii}x+1$$

which is the same equation as we got when we read the y-intercept from the graph.

To summarize how to write a linear equation using the slope-interception form you

Identify the slope, m. This can be washed by calculating the slope between two known points of the line using the slope formula.
Find the y-intercept. This can be done past substituting the slope and the coordinates of a point (x, y) on the line in the gradient-intercept formula and then solve for b.

Once y'all've got both m and b yous can only put them in the equation at their respective position.