Find an equation for the line parallel to 4 y + 28 x = 32 and goes through the point ( 6 , 4 ) . Write your answer in the form y = m x + b

Answer 1

Two lines are parallel if they have the same slope, but go through different points. To find a line parallel to the equation 4y + 28x = 32, it's best to convert it to slope-intercept form (y = mx + b) since we can more easily identify the slope m. To do so, we'll solve the equation for y as follows:

4y + 28x = 32

-28x -28x -> Subtract the x term from both sides so x and y are isolated

4y = -28x + 32

/4 /4 /4 -> Divide all terms in the equation by 4 to get y by itself

y = -7x + 8 -> This is our equation in slope-intercept form! (y = mx + b)

Now we can see from the slope-intercept form that our slope m is -7, so our parallel line also has slope -7. This means our parallel line will have the form y = -7x + b, but how do we find b? Thankfully, the problem tells us that (6, 4) is a point on the line, so all we have to do is plug in this (x, y) value in to the equation and solve for b:

y = -7x + b -> The form of our equation

4 = -7(6) + b -> Plugging our point into the equation

4 = -42 + b

+42 +42 -> Add 42 to both sides to isolate b

46 = b or b = 46 -> The intercept!

So our final equation is y = -7x + 46. If you want to make certain that this equation is correct, you can use a graphing calculator (Desmos is online and completely free) to plot both lines. They should be parallel, and our line should go through both the points (6,4) and (0, 46), as b represents the y-intercept.

Answer 2

4y + 28x = 32

divide by 4

y + 7x = 8

solve for y

y = -7x + 8, which has slope = -7

any parallel line has the same slope but a different y intercept

y = -7x + b. to solve for b plug in the point (6,4)

4 = +7(6) + b

b = 4+42 = 46

y = -7x +46 is the parallel line through the given point