The slope and the y-intercept of a line can be found graphically and mathematically. Use the slope equation and the slope intercept equation to find both variables mathematically, or view the graph of the line to determine the y-intercept and the slope.
- Choose two sets of points
The first step in finding the slope and the y-intercept of a line is to choose two sets of points from the graphed line. Write the two point sets on a piece of paper, and label them point set A and point set B.
- Find the slope
To find the slope of the line from the two point sets solve the following equation: change in y/change in x. Subtract the y value from point set A from the y value of point set B to find the change in the y values. Subtract the x value from point set A from the x value of point set B to find the change in x. Divide the change in y by the change in x to find the slope. To find the slope graphically, use the rise/run equation.
- Find the y-intercept graphically
To find the y-intercept graphically, simply look at the graph and determine where the line passes through the y-axis. This point is the y-intercept.
- Find the y-intercept mathematically
To find the y-intercept mathematically, plug the slope of the line and one set of points into the slope intercept equation, y=mx+b. The b variable is the y-intercept. Solve for b to find the intercept.