6.2 Using Intercepts

We use many different techniques to graph lines, but one of the most efficient and straightforward, when given the equation of the line, is graphing lines using intercepts.

The intercepts are where a graph crosses the x and y axes.

The y-intercept is the y-coordinate of the point where the graph intersects the y-axis. The x-coordinate of this point is ALWAYS zero.   The x-intercept is the x-coordinate of the point where the graph intersects the x-axis. The y-coordinate of this point is ALWAYS zero.

Find the x- and y-intercepts. 5x - 2y = 10

Use intercepts to graph the line described by each equation. 2. 3x - 7y = 21

3. y = -x + 4

Trish runs at 8 meters per second and is running the 200-meter dash. The function f(x) = 200 - 8x gives the distance remaining to run after x seconds. Graph this function and find the intercepts. What does each intercept represent? Y-Intercept represents the starting distance of 200 meters DISTANCE X-Intercept represents the number of seconds it takes Trish to run 200 meters-25 seconds SECONDS

5. An amateur filmmaker has $6000 to make a film that costs $75/h to produce. The function f(x) = 6000 - 75x gives the amount of money left to make the film after x hours of production. Graph this function and find the intercepts. What does each intercept represent? Y-Intercept represents the amount of money he begins with. COST ($) X-Intercept represents the number of hours it will take the filmmaker to use all of his money-80 hours. HOURS