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Line
v has an equation of
y=-(1)/(5)x+9. Line
w includes the point
(-10,1) and is parallet to line
v. What is the equation of line w?

Line $v$ has an equation of $y=-\frac{1}{5} x+9$ . Line $w$ includes the point $(-10,1)$ and is parallet to line $v$ . What is the equation of line w?

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Write equations of cosine functions using properties

Full solution

Q. Line

v

has an equation of

y=-\frac{1}{5} x+9

. Line

w

includes the point

(-10,1)

and is parallet to line

v

. What is the equation of line w?

Identify Slope of Line $w$ : Since line $w$ is parallel to line $v$ , it will have the same slope as line $v$ . The slope of line $v$ is the coefficient of $x$ , which is $-\left(\frac{1}{5}\right)$ .
General Form of Line Equation: The general form of the equation of a line is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept. Since we know the slope of line $w$ is $-\left(\frac{1}{5}\right)$ , we can write its equation as $y = -\left(\frac{1}{5}\right)x + b$ , where $b$ is the y-intercept we need to find.
Find Y-Intercept using Point: To find the y-intercept $b$ , we can use the point $(-10,1)$ which lies on line $w$ . We substitute $x$ with $-10$ and $y$ with $1$ into the equation $y = -\frac{1}{5}x + b$ and solve for $b$ . $\newline$ $1 = -\left(\frac{1}{5}\right)(-10) + b$ $\newline$ $(-10,1)$ $0$ $\newline$ $(-10,1)$ $1$ $\newline$ $(-10,1)$ $2$
Write Final Equation of Line w: Now that we have the slope and the y-intercept, we can write the final equation of line w. It is $y = -\frac{1}{5}x - 1$ .

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