Question

people help me put (-3,5) (2,8)
in y=mx +b form please?

Answer 1

go diradelta go :D

Answer 2

Remember
Slope = change in Y divided by change in X = (8-5)/(2-(-3)) = 3/5

Then we can use something called point slope to fill in the rest, I'll let you figure that part out :). Check your text book

Answer 3

no diradelta don't leave me :( i am stuck at that part it says i can use either (-3,5) or (2,8) to fill in for y and x to solve for b


but i am not good with the arithmetic \[5=\frac{ 3 }{ 5}-3+b ......and 8=\frac{ 3 }{ 5 }2+b\] suppose to be 34/5

Answer 4

Now that you've got your slope, you have the equation
\[y = \frac{ 3 }{ 5 }x + b\]
You can pick either point and plug in the x and y values to solve for b. The two equations you wrote are correct:
\[5 = (\frac{ 3 }{ 5 })(-3) + b\ = \frac{ -9 }{ 5 } + b\]
and
\[8 = (\frac{ 3 }{ 5 })(2) + b\ = \frac{ 6 }{ 5 } + b\]
To solve these equations we need to isolate b by moving all of the other terms to the other side of the equation. In each case, we subtract the constant on the side of the equation with b from both sides to get b by itself.

\[5 - \frac{ -9 }{ 5 } = \frac{ -9 }{ 5 } - \frac{ -9 }{ 5 } + b\]
and

\[8 - \frac{ 6 }{ 5 } = \frac{ 6 }{ 5 } - \frac{ 6 }{ 5 } + b\]
Now we simplify these two equations by converting the whole numbers to their value in 5ths and combining all of the constants. Notice that on the b side of the equation this is going to give us a constant value of 0.

\[5 - \frac{ -9 }{ 5 } = \frac{ 25 }{ 5 } + \frac{ 9 }{ 5 } = \frac{ 34 }{ 5 } = b\]
and
\[8 - \frac{ 6 }{ 5 } = \frac{ 40 }{ 5 } - \frac{ 6 }{ 5 } = \frac{ 34 }{ 5 } = b\]
Now we have the value of b. Notice that in both cases, we got the same number.
Finally, plug b into the y = mx + b form to get the final function:
\[y = \frac{ 3 }{ 5 }x + \frac{ 34 }{ 5 }\]

Answer 5

great explaination blacksteel man, but i am stumped at the " converting the whole numbers to their 5ths and combining all of the constants"

is there another step for getting the answer that i could use?

Answer 6

thank you blacksteel and diracdelta for your answers :D!

Answer 7

We do have to do that step to get the answer, but I glazed over some of the algebra; maybe having that example will help.
To convert a number to its fractional equivalent, we multiply the number by \[\frac{ n }{ n }\] where n is the denominator we want.
Basically,\[1 = \frac{ 2 }{ 2 }= \frac{ 3 }{ 3 }= \frac{ 4 }{ 4 } = ...\]
We can always multiply a number by 1, or something equal to 1, without changing its value.
Let's use one of the problems above. We need to solve \[8 - \frac{ 6 }{ 5 }\] So we start by converting 8 to its equivalent value in 5ths.\[8 = 8*1 = 8*\frac{ 5 }{ 5 } = \frac{ 8*5 }{ 5 } = \frac{ 40 }{ 5 }\] Now we substitute this value into the equation above and simply subtract:\[8 - \frac{ 6 }{ 5 } = \frac{ 40 }{ 5 } - \frac{ 6 }{ 5 } = \frac{ 40 - 6 }{ 5 } = \frac{ 34 }{ 5 }\]

Does this help?

Answer 8

(-3,5) (2,8)