Question

donnas teacher asked her to create 3 equations in standard form that convert to equations in slope-intercept form with only integer values. which of her equations is incorrect?
15x - 5y = 150
7x - y = 147
6x + 4y = 24
2x - 2y = 174

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a linear equation is $y=mx + b$, where $m$ (slope) and $b$ (y - intercept) are integers. To convert a standard form equation $Ax+By = C$ ($A$, $B$, $C$ are integers, $B
eq0$) to slope - intercept form, we solve for $y$: $By=-Ax + C\Rightarrow y=-\frac{A}{B}x+\frac{C}{B}$. For $m =-\frac{A}{B}$ and $b=\frac{C}{B}$ to be integers, $\frac{A}{B}$ and $\frac{C}{B}$ must be integers.

Step2: Analyze $15x - 5y=150$

Solve for $y$:
$- 5y=-15x + 150$
Divide both sides by $-5$: $y = 3x-30$. Here, $m = 3$ (integer) and $b=-30$ (integer).

Step3: Analyze $7x - y=147$

Solve for $y$:
$-y=-7x + 147$
Multiply both sides by $-1$: $y = 7x-147$. Here, $m = 7$ (integer) and $b=-147$ (integer).

Step4: Analyze $6x + 4y=24$

Solve for $y$:
$4y=-6x + 24$
Divide both sides by $4$: $y=-\frac{6}{4}x + 6=-\frac{3}{2}x + 6$. Here, $m=-\frac{3}{2}$ (not an integer).

Step5: Analyze $2x - 2y=174$

Solve for $y$:
$-2y=-2x + 174$
Divide both sides by $-2$: $y=x - 87$. Here, $m = 1$ (integer) and $b=-87$ (integer).

Answer:

The equation $6x + 4y = 24$ is incorrect. So the answer is the option with $6x + 4y = 24$.