The equation of line j is 8x+3y= – 12. Line k, which is perpendicular to line j, includes the point ( – 4, – 1). What is the equation of line k?

Answer 1

In order to determine the slope of line k, you first need to find the slope of line j. Transform the equation of line j to slope intercept form to determine its slope.

8x + 3y = -12

3y = -8x - 12

y = (-8/3)x - 4

So the slope of line j is -8/3.

Since line k is perpendicular to line j, the slope of k is 3/8 (because perpendicular lines have slopes that are negative reciprocals, i.e. the product of those slopes is -1).

Since line k passes through the points (-4, -1) you can use point-slope or slope-intercept to determine its equation (I prefer to use point-slope).

y - (-1) = (3/8) [x - (-4)]

y + 1 = (3/8)(x + 4)

y + 1 = (3/8)x + 3/2

y = (3/8)x + 1/2

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If you choose to use slope-intercept:

-1 = (3/8)(-4) + b

-1 = -3/2 + b

b = -1 + 3/2 = 1/2

Therefore:

y = (3/8)x + 1/2

Answer 2

The equation of the line J is 8x + 3y = -12. Line K, which is perendicular to the line J, includes the point (-4,-1). What is the equaion of the line K?

The equation of the line K, which is perpendicular to line J and passes through the point (-4,-1).

Given information in the problem:

The equation of the line J is 8x + 3y = -12

The line K is perpendicular to the line J

The line K passes through the point (-4,-1)

Formula Information:

The slope intercept form of the linear equation = y = mx +b

m = slope b = y intercept

The slope of the line perpendicular = - 1/m

Step 1: Find the slope of line J

Rewrite the equaion of line J in intercept form

8x + 3y = -12

3y = - 8x - 12

y = -8/3 x - 4

The slope of the line J = - 8/3

Step 2: Find the slope of the line K

Line K is perpendicular to the line J

The slope is the negative reciprocal of the slope of the line J

Slope K = -1 divided by -1/8 slope K = 3/8

Step 3:

Use the slope form to find the equation of the line K

The point slope form of a linear equation is (y-y1) = m (x -x1) where (x1, y1) is the point on the line

and m is the slope.

Substitute the point (-4,-1) and the slope K = 3/8 into the point slope form

y-(-1) 3/8 times [x - (-4)]

negative times negative = positive

y + 1 = 3/8 times (x + 4)

Step 4:

Convert the equation to standard form Ax + By = C

8 (y + 1) = 3 (x +4) multiple both sides of the equation

8y + 8 = 3x + 12

Rearrange the equation to the standard form

Ax + By = C

(Subtract 8 from both sides) 8y + 8 = 3x + 12 = 8y = 3x + 12-8

(Subtract 3x from both sides) 8y = 3x + 4 = -3x + 8y = 4

-

Multiply by - 1: -1(-3x + 8y = 4) = 3x -8y = -4

Final answer : 3x - 8 y = -4

Solution:

The equation of the line K is 3x - 8y = -4

I hope the mathematical calculations (step by step approach) was helpful. Please let me know if you require any more assistance. If anyone in my neighborhood is interested in setting up an in-person math tutoring session. I look forward to hearing from them. Have an amazing day. Doris H.

Answer 3

In order to find the equation of line k you need the slope and a point that line k passes through.

If line k is perpendicular to line j then the product of the slopes is negative 1 right? Also the slope of line j can be found using -(coeff of y)/(coeff of x) = -b/a.

(Slope of line k)*(Slope of line j) = -1

Find the slope of the line k using the above fact. You already have a point (-4,-1) that line k is passing through.

Now finally use the slope - point form y - y1 = m(x - x1). Plug (-4,-1) for (x1,y1).

I hope this helps.