This table gives a few (x, y) pairs of a line in the coordinate plane.
what is the y-intercept of the line?

The Y-intercept is the Y value when X = 0.

Find the change in X:

-56 to -42 = 14

-42  to -28 = 14

The X value changes by 14.

For every change in X the Y change:

66-58 = 8

58-50 = 8

For X to get from -28 to 0 would be 2 more changes:

-28 +14 = -14

-14 + 14 = 0

2 more changes of Y would be:

50-8 = 42

42-8 = 34

So when X = 0, Y = 34

The Y-intercept would be (0,34)

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

Where "m" is the slope and "b" is the y-intercept.

Given the table shown in the image, we can find "m" with this formula:

We can say that:

Then:

Finally, you need substitute the slope and any point on the line into   and solve for "b":

Since the line intersects the y-xis when , then the point is:

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

equation image indicator

x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

equation image indicator

x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

equation image indicator

x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!