What is the equation of a line that is perpendicular to the given line and has an x-intercept of 6?

y = 4/3(x) - 8

Step-by-step explanation:

First we have to find the equation for the given line (I use y = mx + b for everything, although I think it can be done with other formats). The equation for slope is (y2 - y1)/(x2 - x1) = m, so we'll start with that.

(-2 - 4) / (4 - (-4)) = m

-6 / 8 = m

m = -3/4

Now, let's find the rest of the equation. We can do this by treating b as the unknown variable it is, and plugging in a known xy pair, then simply solving for the unknown variable.

y = mx + b; y = 4, x = -4, m = -3/4

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

4 = 3 + b

b = 1

Now we have the original line's equation, y = -3/4(x) + 1. We need to find the new line's slope by finding the negative reciprocal of the base line's. For that, we simply flip the numerator and denominator, then multiply it by -1, to get 4/3. Now we find b again, using the point (6, 0).

y = mx + b; y = 0, x = 6, m = 4/3

0 = 4/3(6) + b

0 = 8 + b

b = -8

This makes our final answer y = 4/3(x) - 8.

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.