In the xy-plane, line is defined by 2ax + 5y = 10, where a is a constant. Line is parallel to the line defined by 4x - 10y = 7. What is the x-intercept of line ?

SAT Linear equations in two variables Practice Question 16 (Hard)

Question bank / Linear equations in two variables

Math · AlgebraHard

In the $xy$ -plane, line $\ell$ is defined by $2ax + 5y = 10$ , where $a$ is a constant. Line $\ell$ is parallel to the line defined by $4x - 10y = 7$ . What is the $x$ -intercept of line $\ell$ ?

$(-5, 0)$

$(5, 0)$

$(0, 2)$

$\left(-\frac{5}{2}, 0\right)$

Show answer and explanation

Answer: A

The line $4x - 10y = 7$ has slope $\frac{4}{10} = \frac{2}{5}$ . Line $\ell$ has slope $-\frac{2a}{5}$ , so $-\frac{2a}{5} = \frac{2}{5}$ and $a = -1$ . Then $\ell$ is $-2x + 5y = 10$ ; setting $y = 0$ gives $x = -5$ .

Choice B comes from a sign error that gives $a = 1$ instead of $a = -1$ .

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