Question

cam was working on a problem that required rewriting an equation. the equation was $y = -\frac{3}{2}x - 18$. the directions asked the student to rewrite the equation in point - slope form, and then in standard form.\
step 1: $y = -1.5x - 18$\
step 2: determine that a point on the line is $(2, -21)$.\
step 3: $y - 2 = -1.5(x + 21)$ this is the point - slope form.\
step 4: $y = -1.5x - 18$\
step 5: $2(y = -1.5x - 18)$\
step 6: $2y = -3x - 36$\
step 7: $3x + 2y = -36$ this is the standard form.\
what step did cam do incorrectly, and how?\
\bigcirc step 3; cam put an $x$-value in place of $y_1$, and a $y$-value in place of $x_1$\
\bigcirc step 7; the equation should be $-3x + 2y = -36$\
\bigcirc step 2; the point $(2, -21)$ is not on the line represented by $y = -1.5x - 18$\
\bigcirc step 1; the slope is $\frac{3}{2}$, not $-1.5$

Explanation:

Step1: Recall point-slope form

The point-slope form is $y - y_1 = m(x - x_1)$, where $(x_1,y_1)$ is a point on the line, and $m$ is the slope.

Step2: Verify the given point

Substitute $x=2$ into $y=-1.5x-18$: $y=-1.5(2)-18=-3-18=-21$. So $(2,-21)$ is valid.

Step3: Analyze Step 3 error

Cam wrote $y - 2 = -1.5(x + 21)$. For point $(2,-21)$, $x_1=2$, $y_1=-21$, so the correct form is $y - (-21) = -1.5(x - 2)$ or $y + 21 = -1.5(x - 2)$. Cam swapped $x_1$ and $y_1$, using $x_1=-21$ and $y_1=2$ incorrectly.

Step4: Rule out other options

• Step1: $-\frac{3}{2}=-1.5$, so this is correct.
• Step2: The point is valid as shown, so this is wrong.
• Step7: Standard form is $Ax+By=C$ with $A\geq0$. $3x+2y=-36$ is correct, so this is wrong.

Answer:

Step 3; Cam put an x-value in place of $y_1$, and a y-value in place of $x_1$