Question 518·Medium·Algebra

0 / 700

In the $xy$ -plane, line $m$ passes through the point $(3,2)$ and is parallel to the line $y = -2x + 5$ . Which equation defines line $m$ ?

The word parallel tells you to keep the same slope, the change in $y$ for each $1$ step in $x$ . Read the slope from the coefficient of $x$ , then use the given point to find the new $y$ -intercept. A Desmos regression can find that intercept. Don't copy the first line's intercept: parallel lines can sit at different heights.

Hints

Hint 1
In slope-intercept form $y=mx+b$ , the number multiplying $x$ is the slope. Parallel lines keep that number, even though they can cross the $y$ -axis at different places. What is the given line's slope?
Hint 2
The intercept $b$ is the value of $y$ when $x=0$ . The given point has $x=3$ , so its $y$ -value is not automatically $b$ . Put the point's coordinates into your new line's equation.
Hint 3
A Desmos regression uses $\sim$ in place of $=$ to find an unknown value. Once you've written an equation using the point, which intercept does Desmos report under PARAMETERS?

Step-by-step

Keep the slope and find the new intercept
Step 1
Read the given line's slope
In slope-intercept form $y=mx+b$ , $m$ is the slope: the change in $y$ for each $1$ increase in $x$ . Type $y=-2x+5$ in Desmos. Its graph falls as $x$ grows, and the coefficient of $x$ gives its slope, $-2$ .
Step 2
Give line $m$ the same slope
Parallel lines run in the same direction, so they have the same slope. Line $m$ needs slope $-2$ too. Don't change the sign or flip the fraction; those moves would give it a different slope.
Step 3
Turn the point into an equation
Write line $m$ as $y=-2x+b$ , where the intercept $b$ is its $y$ -value when $x=0$ . The point $(3,2)$ means $y=2$ when $x=3$ , so $2=-2(3)+b$ . Keep the slope; use the point to find the new intercept. The $+5$ belongs to the other line.
Step 4
Find the new intercept
Type $2\sim-2(3)+b$ in Desmos. The regression symbol $\sim$ asks it to find the unknown intercept that makes the equation true. Desmos shows $b=8$ under PARAMETERS.
Step 5
Match the equation
Type $y=-2x+8$ in Desmos. Its graph runs parallel to the given line, and $8$ is the intercept that makes it pass through $(3,2)$ . So line $m$ is $y=-2x+8$ . Choice D.

Question 518·Medium·Algebra

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this