Since you’re dealing with a linear equation in slope-intercept form, we know the equation is going to be in the form of y=mx+b.
Therefore, we need to find the slope (“m”) of the line (change in y/change in x), which is rise/run. We also need to find the y-intercept (“b.”)
1.) (0, -3) (1, -1) We took two points from the line to find the slope. We will use the 2 coordinate pairs to find the slope.
2.) m=(y2-y1)/(x2-x1) This is the slope “m” formula.
3.) m=( -1+3)/(1-0) Input the coordinate values into the formula. The +3 you see is due to -(-3)=+3.
4.) m=2/1 We simplified the above formula.
5.) m=2 By division.
We now have the slope or “m.” M=2. Therefore, the equation rises 2 units and runs 1 unit.
Now, finding the y-intercept:
The y-intercept or “b” is where the line intersects the y-axis. It is the starting point of a linear equation.
To find the y-intercept, we need to figure out what the output is when the input is 0. We can see on the table in the picture that with an input of 0, the output is -3.
Therefore, b=-3. This is because an input of 0 means that there is no movement on the x-axis, so we can determine where the where the linear intercepts the y-axis.
Therefore, the equation is y=2x-3, where m=2 and b=-3.
