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The equation of line $t$ is $y = -\frac{1}{7}x - 2$ . Parallel to line $t$ is line $u$ , which passes through the point $(7,6)$ . What is the equation of line $u$ ? $\newline$ Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

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Write an equation for a parallel or perpendicular line

Full solution

Q. The equation of line

t

is

y = -\frac{1}{7}x - 2

. Parallel to line

t

is line

u

, which passes through the point

(7,6)

. What is the equation of line

u

?

\newline

Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Determine slope of line t: Determine the slope of line t. $\newline$ The equation of line t is given as $y = -\frac{1}{7}x - 2$ . The slope-intercept form of a line is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept. Comparing the given equation with the slope-intercept form, we can see that the slope ( $m$ ) of line t is $-\frac{1}{7}$ .
Find slope of line $u$ : Since line $u$ is parallel to line $t$ , it will have the same slope. Parallel lines have the same slope. Therefore, the slope of line $u$ will also be $-\frac{1}{7}$ .
Use point-slope form: Use the point-slope form to find the equation of line $u$ . The point-slope form of a line is $y - y_1 = m(x - x_1)$ , where $m$ is the slope and $(x_1, y_1)$ is a point on the line. We know that line $u$ passes through the point $(7,6)$ and has a slope of $-\frac{1}{7}$ . Plugging these values into the point-slope form gives us: $y - 6 = -\frac{1}{7}(x - 7)$ .
Simplify equation to slope-intercept form: Simplify the equation to get it into slope-intercept form. Distribute the slope on the right side of the equation: $y - 6 = -\frac{1}{7}x + 1$ . Now, add $6$ to both sides to solve for $y$ : $y = -\frac{1}{7}x + 1 + 6$ . Combine like terms: $y = -\frac{1}{7}x + 7$ .

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