(05.02) A line passes through (2,8) and (3, 12).
1. What is the slope of this line?
2. What is the y-intercept (show/explain how you know)
3. What is the equation of this line?

1. the slope is 4

2. the y intercept is 0

3. the equation of the line is y=4x

Step-by-step explanation:

First let's find the slope of the line (m)

Let's use the formula (y2-y1)/(x2-x1)

here are the points: (2,8) and (3,12)

let's label them

x1=2

y1=8

x2=3

y2=12

now substitute into the equation.

m=(12-8)/(3-2)

m=4/1

m=4

The slope of the line is 4.

Now, to find the y intercept:

You might have noticed that to go from (2,8) to (3,12), you add 1 to x and 4 to y.

Therefore, to find the y intercept, where the line crosses the y axis, you can first subtract 1 from x and 4 to y to get another point that fits on the line (1,4) and then again to get the point: (0,0)

therefore, the y intercept is 0

the most common method of the equation of the line is y=mx+b, where m is the slope and b is the y intercept

therefore the equation of the line is y=4x+0 or y=4x

Hope this helps!

48 / 6 = x

in this case, x will equal the amount of money in each card!

x therefore will be 8.

trent had $8 in each birthday card.

if gloria has "carry over" minutes, (that is, any minutes paid for but not used in a month can be applied to her payment for minutes in the next month,) her total usage for the three months is: total minutes = 320 + 243 + 489 = 1052 minutes number of 200 minute blocks = 1052/200 = 5 r52 (that is 5 with a remainder of 52) rounding up the number of 200 minute blocks gives her usage for the three months as 6 blocks. the cost for six blocks is 6 x $25 = $150 she also has 200 - 52 or 148 carry over minutes if gloria pays each month and unused minutes are lost, applying the rounding up procedure to each month gives: first month usage of 320 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 second month usage of 243 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 third month usage of 489 minutes rounds up to 3 blocks of 200 minutes for a payment of 3 x $25 = $75 total payments for the three months are $50 + $50 + $75 = $175 get the plan with carry over minutes!