Which equation has the same graph in the xy-plane as y = -23x... | SAT Linear equations in two variables Question, Answer Explained

Math · AlgebraMedium

Which equation has the same graph in the $xy$ -plane as $y = -\frac{2}{3}x + 4$ ?

$2x + 3y = 4$

$2x - 3y = 12$

$3x + 2y = 12$

$2x + 3y = 12$

Show answer and explanation

Answer: D

Multiply both sides of $y = -\frac{2}{3}x + 4$ by $3$ : $3y = -2x + 12$ . Add $2x$ to both sides: $2x + 3y = 12$ .

Choice A multiplies the $x$ -term and $y$ by $3$ but leaves the constant $4$ unchanged.

Why the other choices are wrong

A. This multiplies y and the x-term by 3 but not the constant 4. Its graph has a y-intercept of 4/3, not 4.
B. This loses the negative sign on the slope. The graph of 2x - 3y = 12 has a slope of 2/3.
C. This switches the coefficients of x and y, which gives a slope of -3/2.

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