The graph shows the relationship between the number of science articles, , and the number of history articles, , that can be included in a magazine issue. Which equation could represent this relationship?
To match a graph with a two-variable linear equation, look for an intercept, where the line crosses an axis. Read the y-axis crossing, set in each choice, and check which equation gives the graphed -value. The number on the right is not automatically the y-intercept; the coefficient of matters.
Hints
- Hint 1
The -intercept is where the line meets the vertical axis. The science-article count is zero there. What history-article count does the graph show at that crossing?
- Hint 2
A point is a solution of an equation if its coordinates make both sides equal. Put the intercept’s complete pair of coordinates into each choice, not only its history-article count.
Step-by-step
Test the y-intercept
Step 1Read the crossing on the y-axis
No Desmos needed. The graph’s y-axis crossing gives you a quick way to test the choices. The -intercept is where the line meets the vertical axis. There are science articles at that crossing, and the graph shows history articles, so the line passes through .
- Step 2
Turn the crossing into a test
In standard form, , the coefficient is the number multiplying . A matching equation must work for . Substitute both coordinates:
Remove the zero term:
Test the whole intercept point, not the number on the right by itself.
- Step 3
Check the choices
Use to test the four choices in order:
Only fits the graphed relationship between science and history articles. Choice C.