Question 681·Easy·Math

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In the $xy$ -plane, the graph of a linear function $g$ has a slope of $-4$ and passes through the point $(0,7)$ . Which equation defines $g$ ?

A linear function can be written as $g(x)=mx+b$ : $m$ is the slope, and $b$ is the output when $x=0$ . A given point with input $0$ gives you $b$ directly. Put the slope in front of $x$ and that output at the end. Swapping the two numbers gives a different line.

Hints

Hint 1
A linear function has one term that changes with $x$ and another that stays fixed. At an input of $0$ , think about which term disappears. Keep the changing and fixed parts distinct as you interpret the point.
Hint 2
The slope describes how the output changes when the input increases by $1$ . Would a negative slope make the output rise or fall? Use that direction to check the sign of the term involving $x$ .

Step-by-step

Use the slope and the point at $x=0$
Step 1
Read the constant from the point
No Desmos needed. The slope and the point with $x=0$ give both parts of the rule directly. The point $(0,7)$ means $g(0)=7$ . In $g(x)=mx+b$ , the constant $b$ is the output at $x=0$ , so $b=7$ . A point with input $0$ gives the constant, not the number multiplying $x$ .
Step 2
Put the slope in front of $x$
The slope is the change in output when $x$ increases by $1$ . The given slope is $-4$ , so $m=-4$ . Put it in front of $x$ and use $b=7$ from the point:
$g(x)=-4x+7.$
This defines $g$ with the given slope and point. Choice B.

Question 681·Easy·Math

Strategy

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Step-by-step

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Strategy

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