CEMC Fermat, 2019

Algebra Difficulty 2.4 Junior Find the answer Canada

Line $\ell$ is perpendicular to the line with equation $y=x-3$ . Line $\ell$ has the same $x$ -intercept as the line with equation $y=x-3$ . The $y$ -intercept of line $\ell$ is

Pick one

Solution

The line with equation $y=x-3$ has slope 1.

To find the $x$ -intercept of the line with equation $y=x-3$ , we set $y=0$ and solve for $x$ to obtain $x-3=0$ or $x=3$ . Thus, line $\ell$ also has $x$ -intercept $3$ .

Further, since the two lines are perpendicular, the slopes of the two lines have a product of $-1$ , which means that the slope of $\ell$ is $-1$ .

Line $\ell$ has slope $-1$ and passes through $(3,0)$ .

This means that $\ell$ has equation $y - 0 = -1(x-3)$ or $y = - x+3$ .

Therefore, the $y$ -intercept of line $\ell$ is 3.

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