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Line $c$ has an equation of $y = -5x + 3$ . Parallel to line $c$ is line $d$ , which passes through the point $(2,-6)$ . What is the equation of line $d$ ? $\newline$ 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. Line

c

has an equation of

y = -5x + 3

. Parallel to line

c

is line

d

, which passes through the point

(2,-6)

. What is the equation of line

d

?

\newline

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

Find Slope of Line c: Determine the slope of line c. Line c has an equation of $y = -5x + 3$ . The slope-intercept form of a line is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept. Therefore, the slope of line c is $-5$ .
Determine Slope of Line $d$ : Since line $d$ is parallel to line $c$ , it must have the same slope. Parallel lines have the same slope. Therefore, the slope of line $d$ is also $-5$ .
Find Y-Intercept of Line d: Use the point $(2,-6)$ and the slope $-5$ to find the y-intercept of line $d$ . We can use the point-slope form of the equation of a line, which is $y - y_1 = m(x - x_1)$ , where $(x_1, y_1)$ is a point on the line and $m$ is the slope. Plugging in the point $(2, -6)$ and the slope $-5$ , we get: $-6 - y_1 = -5(2 - x_1)$ Since we are looking for the y-intercept (where $x=0$ ), we can simplify this to find $-5$ $0$ (the y-intercept): $-5$ $1$ $-5$ $2$ $-5$ $3$ $-5$ $4$
Write Equation of Line d: Write the equation of line d in slope-intercept form using the slope $-5$ and the y-intercept $4$ . $\newline$ The slope-intercept form is $y = mx + b$ . Substituting in the slope $-5$ and y-intercept $4$ , we get: $\newline$ $y = -5x + 4$

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