Draw the graphs of y=13x-11 and y=7x+37. When does the first graph lie below the second graph?
{x|x≤ 8 }
Practice makes perfect
To solve the given inequality using a graphing calculator, we need to treat each side of the inequality symbol as its own individual equation.
13x-11 ≤7x+37 ⇒ ly=13x-11 y=7x+37
Then we can look for the values of x where y=13x-11 is less than or equal to y=7x+37. In other words, we want to find the values of x where the graph of y=13x-11 lies below the graph of y=7x+37.
Graphing the Functions
Press Y= on the calculator to access the screen to input our functions.
To draw the graph, press the GRAPH button.
Finding the Solution Set
We see that the graphs intersect at a point. The x-coordinate of this point can be found by pressing 2ND and then CALC.
After selecting the intersect option, we choose the first and second curves. Then, the calculator asks for a guess where the intersection point might be. After that, it will calculate the exact point for us.
The lines intersect at x=8. Tracing the lines on the calculator screen using the TRACE button, we can see that y=13x-11 is the lower line before the intersection. Since the inequality is non-strict, it is also true at the point of intersection. This means that the given inequality holds true when x≤8.
13x-11≤7x+37
⇔
x≤8
We can now write the solution set for the inequality.
{x|x≤ 8 }
