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$The equation for line j can be written as y=-(5)/(7)x-10. Line k, which is parallel to line j, includes the point (-9,5). What is the equation of line k ? Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.$

The equation for line $j$ can be written as $y=-\frac{5}{7} x-10$ . Line $k$ , which is parallel to line $j$ , includes the point $(-9,5)$ . What is the equation of line $k$ ? $\newline$ 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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Algebra 1

Interpret parts of quadratic expressions: word problems

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Q. The equation for line

j

can be written as

y=-\frac{5}{7} x-10

. Line

k

, which is parallel to line

j

, includes the point

(-9,5)

. What is the equation of line

k

\newline

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

Identify slope of line j: Identify the slope of line j. $\newline$ The equation of line j is given as $y = -\left(\frac{5}{7}\right)x - 10$ . The slope of line j is the coefficient of $x$ , which is $-\left(\frac{5}{7}\right)$ .
Determine slope of line $k$ : Determine the slope of line $k$ . $\newline$ Since line $k$ is parallel to line $j$ , it will have the same slope. Therefore, the slope of line $k$ is also $-\left(\frac{5}{7}\right)$ .
Use point-slope form: Use the point-slope form to write the equation of line $k$ . 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 the slope $m$ is $-\frac{5}{7}$ and the point is $(-9, 5)$ .
Substitute slope and point: Substitute the slope and point into the point-slope form. $\newline$ Substituting $m = -\frac{5}{7}$ , $x_1 = -9$ , and $y_1 = 5$ into the point-slope form, we get: $\newline$ $y - 5 = -\frac{5}{7}(x - (-9))$ $\newline$ $y - 5 = -\frac{5}{7}(x + 9)$
Distribute slope and simplify: Distribute the slope and simplify the equation. $\newline$ Distribute $-(\frac{5}{7})$ across $(x + 9)$ : $\newline$ $y - 5 = -(\frac{5}{7})x - (\frac{5}{7})(9)$ $\newline$ $y - 5 = -(\frac{5}{7})x - \frac{45}{7}$
Solve for y: Solve for y to write the equation in slope-intercept form. $\newline$ Add $5$ to both sides of the equation to isolate $y$ : $\newline$ $y = -\frac{5}{7}x - \frac{45}{7} + 5$ $\newline$ $y = -\frac{5}{7}x - \frac{45}{7} + \frac{35}{7}$ $\newline$ $y = -\frac{5}{7}x - \frac{10}{7}$