Question 323·Medium·Algebra

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Which of the following is an equation of the line that passes through the point $(2,-4)$ and has slope $3$ ?

In slope-intercept form $y=mx+b$ , $m$ is the slope and $b$ is the output when $x=0$ . If you're given a slope and a point, put the point into this form, then use a Desmos regression to find $b$ . A match needs both the right slope and the given point. Don't assume the point's $y$ -value is $b$ .

Hints

Hint 1
Use slope-intercept form, $y=mx+b$ , where $m$ is the slope. The given slope tells you the number multiplying $x$ . What does the line's equation look like before you know $b$ ?
Hint 2
A point $(x,y)$ on a line makes its equation true. Put the point's $x$ -coordinate in for $x$ and its $y$ -coordinate in for $y$ to find the missing $b$ .

Step-by-step

Find the intercept from the point
Step 1
Write the line with its known slope
In slope-intercept form $y=mx+b$ , $m$ is the slope and $b$ is the output when $x=0$ . The given slope is $3$ , so $y=3x+b$ .
Step 2
Turn the point into an equation
Passing through $(2,-4)$ means that $x=2$ gives $y=-4$ . Put those values into the line: $-4=3(2)+b$ . The $-4$ isn't automatically $b$ : the point has $x=2$ , not $x=0$ .
Step 3
Find the missing intercept in Desmos
Type $-4\sim3(2)+b$ in Desmos. The $\sim$ tells Desmos to fit the unknown constant $b$ ; under PARAMETERS, it reports $b=-10$ .
Step 4
Match the equation
Put the intercept $b=-10$ into $y=3x+b$ : $y=3x-10$ . This line has the given slope and passes through the given point. Choice D.

Question 323·Medium·Algebra

Strategy

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Step-by-step

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