If a scenario includes a point and a slope, or two points, where neither is the y-intercept, the slope-point form may be useful. (The y-intercept can always be used as a point, but usually the slope-intercept form is chosen when the y-intercept is involved.)

Example 3

Elizabeth drove from Grande Prairie to Lethbridge. Her average speed was 95 km/h and after 7 hours, she had 285 km left to drive.

  1. If x represents the time driven and y represents the distance remaining, write an equation in slope-point form that represents this scenario.

    Elizabeth's distance from Lethbridge decreased at a rate of 95 km/h, so the slope of the line is −95. After 7 hours she had 285 km remaining, so a point on the line is (7,285).



  2. For how long had Elizabeth been driving when there were 650 km left in her trip?



    After approximately 3.16 hours of driving, Elizabeth had 650 km left to drive.

  3. How much farther did Elizabeth have to travel after she had driven for 5.5 hours?



    After 5.5 hours, Elizabeth had 427.5 km remaining.


  4. What is the total distance Elizabeth will drive on her trip from Grande Prairie to Lethbridge?

    The y -intercept represents the total distance of the trip. Set x to zero and solve for y to determine the y-intercept.



    The total distance is 950 km.

  5. How much time will Elizabeth spend driving from Grande Prairie to Lethbridge?

    The x-intercept represents the total time. Set y to zero and solve for x to determine the x-intercept.



    The total time is 10 hours.