How To Find Standard Form From Slope Intercept Form

An equation in the slope-intercept form is written as

$$y=mx+b$$

Where one thousand is the slope of the line and b is the y-intercept. You can use this equation to write an equation if y'all know the gradient and the y-intercept.

Example

Detect the equation of the line

Choose two points that are on the line

Summate the slope between the two points

$$m=\frac{y_{2}\, -y_{i}}{x_{2}\, -x_{1}}=\frac{\left (-1 \right )-3}{iii-\left ( -3 \right )}=\frac{-4}{6}=\frac{-two}{3}$$

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

b = one

We've got a value for grand and a value for b. This gives the states the linear function

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

In many cases the value of b is not equally hands read. In those cases, or if you're uncertain whether the line actually crosses the y-axis in this particular point yous tin calculate b past solving the equation for b so substituting x and y with one of your ii points.

Nosotros can use the example higher up to illustrate this. Nosotros've got the two points (-3, 3) and (three, -one). From these two points we calculated the slope

$$m=-\frac{2}{3}$$

This gives us the equation

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

From this nosotros tin can solve the equation for b

$$b=y+\frac{2}{three}x$$

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

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

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

$$y=-\frac{2}{3}10+1$$

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

To summarize how to write a linear equation using the gradient-interception form yous

Identify the gradient, m. This can be done by computing the slope between two known points of the line using the slope formula.
Find the y-intercept. This tin can be washed by substituting the slope and the coordinates of a point (10, y) on the line in the slope-intercept formula so solve for b.

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