Question

Write the slope-intercept form of the equation for the line.

a. y = 1.4x - 0.6
b. y = -1.4x - 0.6
c. y = -1.4x + 0.6
d. y = 1.4x + 0.6

Medal reward!

Answer 1

Does this line have a positive slope (goes up and to the right) or a negative slope (goes down and to the right)?

Answer 2

Next, what is the y-intercept? That's the spot where the line crosses through the y-axis, and can be calculated exactly given the formula for the line by setting x = 0. Here, you don't know the formula, but you can look at the graph and estimate it.

Answer 3

slope-intercept form requires that we know two pieces of information: the slope, m, and the y-intercept, b

once you know them, the formula will be y = mx + b

as this is a multiple-choice question, knowing whether the slope is positive or negative will allow you to rule out the formulas with the wrong kind of slope, and then you can do the same with the y-intercept to choose correctly between the remaining two answers.

Answer 4

really, all you need here is positive or negative slope? after that, positive y-intercept or negative y-intercept?

Answer 5

The answer is D, because the slope is positive, m=rise/run. y intercept is also positive, at 0.6.

Answer 6

yes, that is a correct answer.

what other one?

Answer 7

Ah, I didn't get a notification that you had posted again. Yes, it's correct.

Answer 8

okay, if you can rearrange it into the form y = kx, then it is direct variation.

2x - 4y = 0
2x = 4y
2x/4 = y
y = x * (2/4) = x*(1/2)

looks like you got it right! or we both made the same mistake :-)

Answer 9

5x = -3y
5x/-3 = y
k = -5/3

looks like you have a good handle on this!

Answer 10

has your teacher told you about indirect and joint variation?

Answer 11

oh, that's right, you mentioned that you were homeschooling. well, if you ever need help figuring something out, just tag me and I'll respond next time I'm on the site.

direction variation (or direct proportionality) is y = kx, as you know.

indirect variation (or inverse proportionality) is y = k/x.

joint variation is z = kxy. if either x or y increases, the quantity increases. if either x or y decreases, the quantity decreases. if one increases and the other decreases, the result depends on how much they vary.

sometimes you'll see things like "varies inversely with the square of the <blank>" this is common in equations describing the physical world. for example, the attractive gravitational force between two masses varies with the square of the distance between their centers. as it turns out, it also varies jointly with the two masses. you can have combined variations like this. the gravity formula is

F = G * m1 * m2
------------
r^2

where G is a constant, m1 and m2 are the two masses, and r is the distance between them.

the F = k/r^2 is inverse or indirect variation with r^2
the F = k m1 m2 is joint variation with m1 and m2

Answer 12

electrostatic repulsion has a very similar formula.