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Line
ℓ in the
xy-plane passes through the point
(-4,5) and is perpendicular to the line with the equation
y=(1)/(2)x+5.
What is the
y-intercept of line
ℓ ?
Select one answer.

-3
5
7
13
Support
PowerSchool Community

Line $\ell$ in the $x y$ -plane passes through the point $(-4,5)$ and is perpendicular to the line with the equation $y=\frac{1}{2} x+5$ . $\newline$ What is the $y$ -intercept of line $\ell$ ? $\newline$ Select one answer. $\newline$ $-3$ $\newline$ $5$ $\newline$ $7$ $\newline$ $13$ $\newline$ Support $\newline$ PowerSchool Community

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Write an equation for a parallel or perpendicular line

Full solution

Q. Line

\ell

in the

x y

-plane passes through the point

(-4,5)

and is perpendicular to the line with the equation

y=\frac{1}{2} x+5

.

\newline

What is the

y

-intercept of line

\ell

?

\newline

Select one answer.

\newline

-3

\newline

5

\newline

7

\newline

13

\newline

Support

\newline

PowerSchool Community

Identify slope: Step $1$ : Identify the slope of the given line. $\newline$ The equation of the line is $y = \frac{1}{2}x + 5$ . The slope $(m)$ of this line is $\frac{1}{2}$ .
Determine perpendicular slope: Step $2$ : Determine the slope of line $\ell$ , which is perpendicular to the given line. $\newline$ Since line $\ell$ is perpendicular to a line with slope $\frac{1}{2}$ , its slope will be the negative reciprocal of $\frac{1}{2}$ , which is $-2$ .
Use point-slope form: Step $3$ : Use the point-slope form to find the equation of line $\ell$ . Line $\ell$ passes through the point $(-4,5)$ and has a slope of $-2$ . 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. Plugging in the values, we get $y - 5 = -2(x + 4)$ .
Simplify to slope-intercept form: Step $4$ : Simplify the equation to slope-intercept form $y = mx + b$ to find the y-intercept. $y - 5 = -2(x + 4)$ $y - 5 = -2x - 8$ $y = -2x - 3$ The y-intercept $b$ of line $\ell$ is $-3$ .

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