Question 368·Medium·Algebra

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When line $r$ is graphed in the $xy$ -plane, it has a slope of $-\tfrac{3}{2}$ and passes through the point $(6,-1)$ . Which of the following is an equation of line $r$ in slope–intercept form?

In slope-intercept form, $y=mx+b$ , the coefficient $m$ is the slope and $b$ is the value of $y$ at $x=0$ . A given slope and a point tell you to write the line with an unknown $b$ , then substitute the point. A Desmos regression can find $b$ . The point’s $y$ -coordinate is not automatically the intercept.

Hints

Hint 1
In slope-intercept form, $y=mx+b$ , the coefficient $m$ is the slope. Put the given slope in place of $m$ . Which part of the equation is still unknown?
Hint 2
A point $(u,v)$ on a line means $x=u$ produces $y=v$ . Substitute both coordinates into the equation. You’ll get one equation whose only unknown is the intercept $b$ .

Step-by-step

Find the intercept from the point
Step 1
Write the line with its given slope
In slope-intercept form, $y=mx+b$ , $m$ is the slope and $b$ is the $y$ -intercept, the value of $y$ at $x=0$ . The given slope fixes the coefficient of $x$ , so $y=-\frac{3}{2}x+b$ . An equation with $-\frac{2}{3}$ on $x$ reverses the slope fraction.
Step 2
Turn the point into an equation
The point $(6,-1)$ means $x=6$ gives $y=-1$ . Substitute both coordinates: $-1=-\frac{3}{2}(6)+b$ . Don’t use $-1$ as the intercept: the point’s $x$ -coordinate is $6$ , not $0$ .
Step 3
Find the intercept in Desmos
Type $-1\sim-\frac{3}{2}(6)+b$ in Desmos. A regression uses $\sim$ in place of $=$ to find the unknown constant. Under PARAMETERS, Desmos shows $b=8$ .
Step 4
Write the requested equation
Put $b=8$ into the line’s equation, keeping the given slope: $y=-\frac{3}{2}x+8$ . That’s line $r$ in slope-intercept form. Choice D.

Question 368·Medium·Algebra

Strategy

Hints

Step-by-step

Lessons that teach this

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Strategy

Hints

Step-by-step

Lessons that teach this