How To Find Slope Intercept Form From A Graph

An equation in the gradient-intercept form is written equally

$$y=mx+b$$

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

Example

Observe the equation of the line

Choose two points that are on the line

Calculate the slope between the two points

$$m=\frac{y_{ii}\, -y_{1}}{x_{two}\, -x_{1}}=\frac{\left (-1 \correct )-3}{three-\left ( -iii \right )}=\frac{-iv}{6}=\frac{-2}{iii}$$

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

b = 1

We've got a value for m and a value for b. This gives usa the linear role

$$y=-\frac{2}{3}x+ane$$

In many cases the value of b is not equally easily read. In those cases, or if yous're uncertain whether the line actually crosses the y-axis in this particular betoken you can calculate b by solving the equation for b and then substituting x and y with one of your two points.

We can utilise the case above to illustrate this. We've got the two points (-3, 3) and (3, -1). From these 2 points we calculated the slope

$$chiliad=-\frac{2}{three}$$

This gives us the equation

$$y=-\frac{2}{3}10+b$$

From this we can solve the equation for b

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

And if we put in the values from our showtime indicate (-three, 3) we get

$$b=three+\frac{ii}{3}\cdot \left ( -3 \correct )=iii+\left ( -2 \right )=one$$

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

$$y=-\frac{2}{3}10+ane$$

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

To summarize how to write a linear equation using the slope-interception grade y'all

Identify the slope, g. This can be done by calculating the slope between ii known points of the line using the slope formula.
Observe the y-intercept. This can be washed by substituting the gradient and the coordinates of a indicate (x, y) on the line in the gradient-intercept formula and and so solve for b.

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