QuestionFind the equation of line $w$ , parallel to $y-6=-\frac{3}{5}(x+2)$ and passing through $(10,3)$ .

Studdy Solution

STEP 1

Assumptions1. Line $v$ has an equation $y-6=-\frac{3}{5}(x+)$ . Line $w$ is parallel to line $v$
3. Line $w$ includes the point $(10,3)$ 4. Two lines are parallel if and only if their slopes are equal

STEP 2

First, we need to find the slope of line $v$ . We can do this by rewriting the equation of line $v$ in slope-intercept form ( $y = mx + b$ ), where $m$ is the slope.
$y-6=-\frac{}{5}(x+2)$

STEP 3

istribute the $-\frac{3}{5}$ to both terms inside the parentheses.
$y-6=-\frac{3}{5}x - \frac{6}{5}$

STEP 4

Add6 to both sides of the equation to isolate $y$ .
$y=-\frac{3}{}x + \frac{24}{}$

STEP 5

Now we see that the slope of line $v$ is $-\frac{3}{5}$ .

STEP 6

Since line $w$ is parallel to line $v$ , it will have the same slope. So, the slope of line $w$ is also $-\frac{3}{5}$ .

STEP 7

To find the equation of line $w$ , we need to find its y-intercept. We can use the point-slope form of a line equation, $y - y1 = m(x - x1)$ , where $(x1, y1)$ is a point on the line and $m$ is the slope.

STEP 8

Substitute the given point $(10,3)$ and the slope $-\frac{3}{5}$ into the point-slope form.
$y -3 = -\frac{3}{5}(x -10)$

STEP 9

istribute the $-\frac{3}{5}$ to both terms inside the parentheses.
$y -3 = -\frac{3}{5}x +6$

STEP 10

Add3 to both sides of the equation to isolate $y$ .
$y = -\frac{3}{5}x +9$ The equation of line $w$ is $y = -\frac{3}{5}x +9$ .

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