What is the equation in slope-intercept form of a line that is perpendicular to y=2x+2 and passes through the point (4, 3)?

Mathematics

1 answer:

andriy [413]2 years ago

7 0

Answer:

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

Step-by-step explanation:

slope-intercept form

y= mx +c, where m is the slope and c is the y-intercept

Given line: y= 2x +2

slope= 2

The product of the slopes of perpendicular lines is -1. Let the slope of the unknown line be m.

m(2)= -1

m= -1 ÷2

m= -½

Substitute the value of m into the equation:

y= -½x +c

To find the value of c, substitute a pair of coordinates.

When x= 4, y= 3,

3= -½(4) +c

3= -2 +c

c= 3 +2

c= 5

Thus, the equation of the line is y= -½x +5.

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