Question Bank / Math / Linear Equations in Two Variables

Linear equations in two variables SAT question

Math · Algebra · Easy · Answer it here, explanation included.

$x$	$y$
$0$	$18$
$1$	$13$
$2$	$8$

The table shows three values of $x$ and their corresponding values of $y$ . There is a linear relationship between $x$ and $y$ . Which of the following equations represents this relationship?

ExplanationShow

Choice D is correct. A linear relationship can be represented by an equation of the form $y = m x + b$ , where $m$ and $b$ are constants. It’s given in the table that when $x = 0$ , $y = 18$ . Substituting $0$ for $x$ and $18$ for $y$ in $y = m x + b$ yields $18 = m (0) + b$ , or $18 = b$ . Substituting $18$ for $b$ in the equation $y = m x + b$ yields $y = m x + 18$ . It’s also given in the table that when $x = 1$ , $y = 13$ . Substituting $1$ for $x$ and $13$ for $y$ in the equation $y = m x + 18$ yields $13 = m (1) + 18$ , or $13 = m + 18$ . Subtracting $18$ from both sides of this equation yields $- 5 = m$ . Therefore, the equation $y = - 5 x + 18$ represents the relationship between $x$ and $y$ .

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Drill this skill on Aceit

Adaptive practice, a daily plan, and score tracking take a free account so we can save your work.

Practice this skill

Linear equations in two variables SAT question

More Linear equations in two variables questions