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41 votes
24. Write the equation of the line that passes through (0, -13) and is perpendicular to the line y = -2x + 5

User Ratul Bin Tazul
by
2.7k points

2 Answers

9 votes
9 votes

Explanation:

The slope of two perpendicular lines is the negative reciprocal of each other.

Given a line y = -2x + 5, the slope of this line is -2. Therefore, the slope of the line perpendicular to this line is 1/2.

Given a slope of 1/2 and a point at (0, -13), let's use the point-slope form of the equation to be able to identify the equation of this line.

y-y_1=m(x-x_1)y−y

1

=m(x−x

1

)

where m = slope.

\begin{gathered}\begin{gathered} y-(-13)=\frac{1}{2}(x-0) \\ y+13=\frac{1}{2}(x) \\ y=\frac{1}{2}x-13 \end{gathered}\end{gathered}

y−(−13)=

2

1

(x−0)

y+13=

2

1

(x)

y=

2

1

x−13

Therefore, the equation of the line that passes through (0, -13) and is perpendicular to the line y = -2x + 5 is y = 1/2x - 13.

User Cristina
by
3.0k points
14 votes
14 votes

The slope of two perpendicular lines is the negative reciprocal of each other.

Given a line y = -2x + 5, the slope of this line is -2. Therefore, the slope of the line perpendicular to this line is 1/2.

Given a slope of 1/2 and a point at (0, -13), let's use the point-slope form of the equation to be able to identify the equation of this line.


y-y_1=m(x-x_1)

where m = slope.


\begin{gathered} y-(-13)=(1)/(2)(x-0) \\ y+13=(1)/(2)(x) \\ y=(1)/(2)x-13 \end{gathered}

Therefore, the equation of the line that passes through (0, -13) and is perpendicular to the line y = -2x + 5 is y = 1/2x - 13.

User Daddyboy
by
2.3k points