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Here are a few recommended readings before getting started with this lesson.
Analyze the graphs of different linear functions. Do these lines have anything in common?
When trying to find similarities between lines, the first group of lines all have the same y-intercept, while the second group of lines have the same slope. These two characteristics can be used to write an equation of any line.
Consider the given linear equation that represents the relation between two variables x and y. Determine whether the equation is written in slope-intercept form.
Tiffaniqua is driving from her home in New York to visit her sister, who lives in Springfield, Missouri. On the first day of the trip, she traveled 250 miles to Washington DC to pick up her friend Maya.
Together they continued traveling 350 miles per day. The number of miles that Tiffaniqua traveled is represented by the following linear equation.Next, by using the slope, the second point on the line can be determined. Since the slope is 350, move 1 unit right and 350 units up from the first point, then plot the new point.
Finally, by drawing the line through the two plotted points, the graph of the equation can be completed.
Note that since m and d represent the number of miles and days, respectively, they cannot have negative values. This is why the line is only drawn in the first quadrant and is actually a ray.
Next, determine the x-coordinate of that point on the line.
From the graph it can be concluded that Tiffaniqua passed the mark of 1200 miles on the second day of traveling together with Maya. Since on the first day Tiffaniqua traveled 250 miles alone to pick up Maya, the second day of traveling together with Maya is her third day of travel in total.
The evening after Tiffaniqua and Maya arrived at Tiffaniqua's sister's house, the girls decided to pass the evening by putting together puzzles. The number of the remaining puzzle pieces as the girls complete the puzzle is shown in the following graph.
On the diagram, p represents the number of puzzle pieces and t represents time spent completing the puzzle in minutes.
Tiffaniqua really wants to make a dress that she has been dreaming about for a long time. In her sister's town, there is a very famous fabric store, so she decided to go there for the necessary fabric.
After choosing the perfect fabric, she asked the shop assistant how much 4 and 6 yards of the fabric would cost. The shop assistant told her that the costs would be $3 and $4.50, respectively.Next, use the slope of 0.75 to plot the second point that lies on the line. Note that 0.75 can be rewritten as 43. Therefore, by moving 4 units right and 3 units up, the second point can be located.
Finally, draw a line through the two points to obtain the graph of the equation.
Note that since it is not possible to buy a negative number of yards of fabric, the line should only be drawn for non-negative values of x.
As can be seen, the points indeed lie on the line.
Given a line, two of its points, or its equation in either standard or point-slope form, write an equation in slope-intercept form.
Determine the slope or y-intercept of a line given its graph, two of its points, or its equation, which may or may not be written in slope-intercept form.