QuestionFind the equation of line $q$ that is parallel to $y=-\frac{5}{6} x-5$ and passes through the point $(9,-4)$ .

Studdy Solution

STEP 1

Assumptions1. Line $p$ has an equation of $y=-\frac{5}{6} x-5$ . Line $q$ includes the point $(9,-4)$ 3. Line $q$ is parallel to line $p$

STEP 2

The slope of a line is the coefficient of $x$ in the line's equation. Since line $q$ is parallel to line $p$ , they have the same slope. So, the slope of line $q$ is $-\frac{5}{6}$ .

STEP 3

The equation of a line in slope-intercept form is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept. We know the slope of line $q$ is $-\frac{5}{6}$ and it passes through the point $(9,-)$ . We can substitute these values into the equation to solve for $b$ .
$- = -\frac{5}{6} \cdot9 + b$

STEP 4

olve the equation for $b$ .
$-4 = -\frac{45}{6} + b$ $-4 = -7. + b$ $b = -4 +7.$ $b =3.$

STEP 5

Now that we have the slope and the y-intercept, we can write the equation of line $q$ .
$y = -\frac{5}{}x +3.5$ The equation of line $q$ is $y = -\frac{5}{}x +3.5$ .

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