Question 101·Medium·Linear Equations in Two Variables
The graph shows a relationship between the number of adult tickets, , and the number of child tickets, , that can be purchased with a budget of $170.
Which equation could represent this relationship?
For a line shown on a graph, use two clear points on the line to compute the slope, then use point-slope form to write an equation. If the answers are in standard form, convert your equation by clearing fractions and rearranging so all and terms are on one side and the constant is on the other.
Hints
Use the labeled points
Pick the two labeled points on the line and write them as ordered pairs.
Compute the slope
Find the slope using with the two points.
Check with substitution
After you have a candidate equation, substitute each labeled point to see whether it makes the equation true.
Desmos Guide
Plot the two points
Enter the points
(10,35)(50,5)
so you can check which equation’s graph goes through both.
Graph each answer choice
Enter each equation (one at a time or all together) exactly as written in the choices.
Match the line to the points
Identify which graphed line passes through both plotted points. The equation for that line is the correct choice.
Step-by-step Explanation
Read two points from the graph
From the graph, the line passes through and .
Find the slope
Compute the slope:
Write the equation and convert to standard form
Use point-slope form with :
Multiply by 4 to clear fractions:
Rearrange:
So the correct choice is .