Question 498·Easy·Algebra

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Which choice is an equation of the line shown in the $xy$ -plane?

A graph with marked points gives you two facts for slope-intercept form: the line’s slope and where it crosses the $y$ -axis. Read the axis crossing first, then use the two points to check the slope. One matching fact alone doesn’t identify a line. If several choices have the same slope, the $y$ -intercept separates them.

Hints

Hint 1
The $y$ -intercept is where the line crosses the vertical axis, so its $x$ -coordinate is $0$ . Which marked point has $x=0$ , and what does its $y$ -coordinate tell you?
Hint 2
The slope compares the change in $y$ with the change in $x$ . From $(0,2)$ to $(6,5)$ , put the $y$ -change on top and the $x$ -change underneath.

Step-by-step

Read the intercept, then check the slope
Step 1
Read where the line crosses the vertical axis
No Desmos needed. The marked points let you read and check the line’s equation directly. The $y$ -intercept is where $x=0$ . The marked point $(0,2)$ is on that axis, so the line’s $y$ -intercept is $2$ .
Step 2
Find the slope from the marked points
The slope is the change in $y$ divided by the change in $x$ . Use $(0,2)$ and $(6,5)$ in the same order on top and bottom:
$m=\frac{5-2}{6-0}$
Subtract:
$m=\frac{3}{6}$
Reduce:
$m=\frac12$
Step 3
Match both parts of the equation
In slope-intercept form, $y=mx+b$ , the slope is $m$ and the $y$ -intercept is $b$ . Use both values you found:
$y=\frac12x+2$
This line has the graph’s slope and passes through $(0,2)$ . Choice A.

Question 498·Easy·Algebra

Strategy

Hints

Step-by-step

Lessons that teach this

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Strategy

Hints

Step-by-step

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