51.1k views
4 votes
HELP ASAP

write an equation in slope-intercept form for the line that passes through (-3,5) and is perpendicular to the graph of y+2x=4

1 Answer

7 votes

Answer:

We conclude that an equation in slope-intercept form for the line that passes through (-3,5) and is perpendicular to the graph of y+2x=4 will be:


\:y=(1)/(2)x+(13)/(2)

Explanation:

Given the line

y+2x=4

converting into the slope-intercept form y = mx+b where m is the slope

y = -2x+4

comparing with the slope-intercept form

Thus, the slope is: m = -2

We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:

slope = m = -2

The slope of the new line perpendicular to the given line = – 1/m

= -1/-2 = 1/2

Using the point-slope form


y-y_1=m\left(x-x_1\right)

where m is the slope of the line and (x₁, y₁) is the point

substituting the values m = 1/2 and the point (-3, 5)


y-y_1=m\left(x-x_1\right)


y-5=(1)/(2)\left(x-\left(-3\right)\right)


y-5=(1)/(2)\left(x+3\right)

Add 5 to both sides


y-5+5=(1)/(2)\left(x+3\right)+5


\:y=(1)/(2)x+(13)/(2)

Therefore, we conclude that an equation in slope-intercept form for the line that passes through (-3,5) and is perpendicular to the graph of y+2x=4 will be:


\:y=(1)/(2)x+(13)/(2)

User Bex
by
8.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories