Question

Comparing Linear Functions Written in Different Ways
Compare the linear functions expressed below by data in a table and by an equation.

A 2-column table with 4 rows. Column 1 is labeled x with entries negative 6, negative four-thirds, 1, 4. Column 2 is labeled y with entries negative StartFraction 9 Over 2 EndFraction, negative 1, three-fourths, 3. y = three-fourths x.

Which of the following statements are true? Select all that apply.
If the equation were graphed, it would be a horizontal line.
Both functions have the same slope.
The origin is the y-intercept for the function expressed in the table.
The linear equation does not have a y-intercept.
The table and the graph express an equivalent function.

Answer 1

True:
- Both functions have the same slope. (Slope = 3/4; e.g. between (1, 3/4) and (4, 3): (3 − 3/4)/(4 − 1) = 3/4.)
- The origin is the y-intercept for the function expressed in the table. (All table points satisfy y = (3/4)x, so y(0)=0.)
- The table and the graph express an equivalent function. (Every table pair lies on y = (3/4)x.)

False:
- If the equation were graphed, it would be a horizontal line. (No — slope is 3/4, not 0.)
- The linear equation does not have a y-intercept. (It does: y-intercept = 0.)