Question 543·Easy·Algebra

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In the $xy$ -plane, line $k$ passes through the point $(3,2)$ and has a slope of $-2$ . Which equation represents line $k$ ?

A given slope and a point cue slope-intercept form, $y=mx+b$ , where $m$ is the slope and $b$ is the $y$ -value at $x=0$ . Put the slope in first, then use the point in a Desmos regression to find $b$ . A line must match both the slope and the point; the point's $y$ -value isn't automatically the intercept.

Hints

Hint 1
In slope-intercept form, $y=mx+b$ , the number $m$ tells you how much $y$ changes when $x$ increases by $1$ . Which part of the equation does the given slope replace?
Hint 2
A point on a line makes its equation true: replace $x$ and $y$ with the point's coordinates. The intercept is the $y$ -value at $x=0$ , so a point with another $x$ -value doesn't give you $b$ directly.

Step-by-step

Find the intercept from the point
Step 1
Put the slope into the line's equation
The slope tells you how $y$ changes when $x$ increases by $1$ . In $y=mx+b$ , the given slope makes $m=-2$ , so $y=-2x+b$ . The point's $y$ -value isn't $b$ because its $x$ -value isn't $0$ .
Step 2
Make the equation fit the point
The point $(3,2)$ means $x=3$ gives $y=2$ . Put both coordinates into $y=-2x+b$ : $2=-2(3)+b$ .
Step 3
Find the missing intercept
Type $2\sim -2(3)+b$ in Desmos. The tilde, $\sim$ , tells Desmos to find the $b$ that fits the equation. Under PARAMETERS, it shows $b=8$ . That's the line's $y$ -value when $x=0$ .
Step 4
Write the equation of line k
Put $b=8$ into $y=-2x+b$ : $y=-2x+8$ . It has the given slope, and the point condition you solved puts $(3,2)$ on the line. Choice D.

Lessons that teach this

SAT AlgebraBeginnerCoreWrite and match linear functions

Question 543·Easy·Algebra

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Step-by-step

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Strategy

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Step-by-step

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