Question

Write an equation in slope-intercept form for the line that passes through the given point and is perpendicular to the following equation.
Point: (−4,−3)

Equation: 4x+y=7

Perpendicular Equation:

Answer 1

Answer: the equation is

y = x/4 -2

Step-by-step explanation:

Write an equation in slope-intercept form for the line that passes through the given point and is perpendicular to the following equation

Slope-intercept equation is

y= mx + c

Point: (−4,−3)

Equation: 4x+y=7

For two lines to be perpendicular, the product of their slopes, m1 and m2 must be equal to -1

From the given equation, 4x+y=7

y = 7-4x, y= -4x +7.

slope,m1 = -4

Slope of second perpendicular line

=m2

m1 × m2 =-1

4 × m2= -1

m2=-1/-4= 1/4

y = x/4+ c

From the points (−4,−3) given,

y = -3 and x = -4

Substituting in the equation, y = -x/4+ c,

-3= 1/4×-4 + c

-3 = -1+c

c = -3+1 = -2

So the equation is

y = x/4 -2

Answer 2

The perpendicular equation would include a slope that is the opposite reciprocal of the original slope.

Steps:
1. Get x to the other side in the original equation. This making the slope -4 or -4/1.

2. Turn the slope into it’s opposite reciprocal m = 1/4.

3. If you use point-slope form, y - y1 = m( x - x1 ), you can substitute y1 and x1 with the numbers in the point given. But since we previously found the opposite reciprocal, we will replace “m” as well. *By the way, the subtraction of a negative makes a positive. [y + 3 = 1/4( x + 4 )]

4. Solve:
A: Distribute (y + 3 = 1/4x + 1)
B: Subtract 3 from both sides (y = 1/4x -2)

Perpendicular Equation: y = 1/4x - 2