CEMC Fermat, 2021

Algebra Difficulty 1.3 Junior Find the answer Canada

The line with equation $y=2x-6$ is translated upwards by 4 units. (That is, every point on the line is translated upwards by 4 units, forming a new line.) The $x$ -intercept of the resulting line is

$3$
$\frac{3}{2}$
$4$
$1$
$2$

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

The line with equation $y=2x-6$ has slope 2. When this line is translated, the slope does not change.

The line with equation $y=2x-6$ has $y$ -intercept $-6$ . When this line is translated upwards by 4 units, its $y$ -intercept is translated upwards by 4 units and so becomes $-2$ .

This means that the new line has equation $y = 2x-2$ .

To find its $x$ -intercept, we set $y=0$ to obtain $0 = 2x - 2$ and so $2x = 2$ or $x=1$ .

Thus, the $x$ -intercept is 1.

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