Question 124·Easy·Linear Functions
The graph of the linear function is shown above, where .
Which choice is the slope of the graph of ?
For a line on a graph, pick two points with clear coordinates and compute slope as . Count (or subtract) the vertical change and the horizontal change, then reduce the fraction if needed.
Hints
Use the marked points
Pick the two plotted points that lie on the line; they have integer coordinates.
Find rise and run
Compute (up or down) and (left or right) between those two points.
Simplify the fraction
Write the slope as and reduce the fraction to lowest terms.
Desmos Guide
Enter the two points
In Desmos, type the points and as separate expressions to show them.
Compute the slope with an expression
Type the expression .
Read the value
Desmos will display the simplified value of the expression; that value is the slope of the line through the two plotted points.
Step-by-step Explanation
Choose two points on the line
Use the two marked points on the graph: and .
Compute rise over run
Compute the change in and the change in :
So the slope is .
Simplify
Simplify to get .
Therefore, the slope is .