QuestionTICE TEST
21 Mark for Review
In the $x y$ -plane, line $\ell$ passes through the point $(0,0)$ and is parallel to the line represented by the equation $y=8 x+2$ . If line $\ell$ also passes through the point $(3, d)$ , what is the value of $d$ ? $\square$
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Studdy Solution

STEP 1

1. Line $\ell$ passes through the origin $(0,0)$ .
2. Line $\ell$ is parallel to the line represented by the equation $y = 8x + 2$ .
3. Line $\ell$ passes through the point $(3, d)$ .
4. We need to find the value of $d$ .

STEP 2

1. Determine the slope of line $\ell$ .
2. Write the equation of line $\ell$ .
3. Substitute the point $(3, d)$ into the equation of line $\ell$ to find $d$ .

STEP 3

Determine the slope of line $\ell$ .
Since line $\ell$ is parallel to the line $y = 8x + 2$ , it has the same slope as this line. The slope of the line $y = 8x + 2$ is $8$ .

STEP 4

Write the equation of line $\ell$ .
Since line $\ell$ passes through the origin $(0,0)$ and has a slope of $8$ , its equation is:
$y = 8x$

STEP 5

Substitute the point $(3, d)$ into the equation of line $\ell$ to find $d$ .
Substitute $x = 3$ into the equation $y = 8x$ :
$d = 8 \times 3$ $d = 24$
The value of $d$ is:
$\boxed{24}$

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