Question

how to find the equation of a linear graph

Answer 1

Writing linear equations using the slope-intercept form

An equation in the slope-intercept form is written as

y=mx+b

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

Example

Find the equation of the line

picture26

Choose two points that are on the line

picture27

Calculate the slope between the two points

m=y2−y1x2−x1=(−1)−33−(−3)=−46=−23

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

picture28

b = 1

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

y=−23x+1

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

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

m=−23

This gives us the equation

y=−23x+b

From this we can solve the equation for b

b=y+23x

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

b=3+23⋅(−3)=3+(−2)=1

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

y=−23x+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 done by calculating the slope between two known points of the line using the slope formula.

Find the y-intercept. This can be done by substituting the slope and the coordinates of a point (x, y) on the line in the slope-intercept formula and then solve for b.

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