Question 138·Easy·Algebra

Remember that the slope of a line is the change in $y$ divided by the change in $x$. Use the pattern you found in the table to find the slope.

Once you know the slope and use the form $y=mx+b$, which point in the table immediately tells you the value of $b$?

In Desmos, add a table and enter the three points from the question: $(0,18)$, $(1,13)$, and $(2,8)$.

Type each option as a separate equation in Desmos: y = 18x + 13, y = 18x + 18, y = -5x + 13, and y = -5x + 18. Each will appear as a line on the graph.

Look at which line goes exactly through all three plotted points from the table. The equation of that line is the correct choice.

Look at how $y$ changes when $x$ increases by 1.

• From $x=0$ to $x=1$: $y$ goes from $18$ to $13$, a change of $13-18=-5$.
• From $x=1$ to $x=2$: $y$ goes from $13$ to $8$, a change of $8-13=-5$.

Because the change in $y$ is always $-5$ when $x$ increases by 1, the slope $m$ is $-5$.

Any linear equation with slope $-5$ can be written as

where $b$ is the $y$-intercept (the value of $y$ when $x=0$).

Use the point where $x=0$, because that directly gives the $y$-intercept.

From the table, when $x=0$, $y=18$.

Substitute $x=0$ and $y=18$ into $y=-5x+b$:

So the $y$-intercept $b$ is $18$. The equation becomes

This matches answer choice D.