# Graphing linear relationship using initial value and slope

- Author:
- Mathguru, Walch Education

- Topic:
- Planes

The velocity (or speed) of a ball thrown directly upward can be modeled with the following equation: = + , where is the speed, is the force of gravity, is the elapsed time, and is the initial velocity at time 0. If the force of gravity is equal to 32 feet per second, and the initial velocity of the ball is 96 feet per second, what is the equation that represents the velocity of the ball? Graph the equation.

- Read the problem statement and then reread the problem, determining the known quantities.
- Identify the slope and the
*y*-intercept. - Substitute the slope and
*y*-intercept into the equation*y*=*mx*+*b*, where*m*is the slope and*b*is the*y*-intercept. - Set up the coordinate plane.
- Graph the equation using the slope and
*y*-intercept. Plot the*y*-intercept first. - Graph the equation using the slope and
*y*-intercept. Use the slope to find the second point. - Connect the points and extend the line. Then, label your line. Draw a line through the two points and add an arrow to the right end of the line to show that the line of the equation continues infinitely in that direction. Label the line with the equation.