Find the equation of the line with a slope of 2.3 and travels through the point (4, 6).
Plug in m=2.3 x=4, y=6 in
y = mx+b
6 = 2.3(4) + b
6 = 9.2 + b
-3.2 = b
Substitute m=2.3, b=-3.2, x=x, y=y in
y = mx+b
y = 2.3x+(-3.2)
y = 2.3x-3.2
* So first I tried to figure out what is m?
You are given m, the slope, as 2.3
what is b?
You find that as I did above, as b=-3.2
Then try to plug them into the formula: y=mx+b. As a result, I found out that m= 2/3, x=4 and y=-6.
Oh, I see. You made a typo and typed 2.3 when you meant to type 2/3.
OK.
Plug in m=2/3 x=4, y=6 in
y = mx+b
6 = (2/3)(4) + b
6 = 8/3 + b
Multiply through by 3 to clear the fraction
18 = 8 + 3b
10 = 3b
10/3 = b
Substitute m=2/3, b=10/3, x=x, y=y in
y = mx+b
y = (2/3)x+(10/3)
The only thing we don't know is what is b.
*-6= 2/3(4)+ b
Why did you substitute -6 for y? You should have substituted 6
because you said above that it travels through (4, 6), not
(4, -6). Did you make another typo on the point?
OK. I'll assume you meant m=2/3 and travels through (4, -6), not (4,6).
Plug in m=2/3 x=4, y=-6 in
y = mx+b
-6 = (2/3)(4) + b
-6 = 8/3 + b
Multiply through by 3 to clear the fraction
-18 = 8 + 3b
-26 = 3b
-26/3 = b
Substitute m=2/3, b=-26/3, x=x, y=y in
y = mx+b
y = (2/3)x+(-26/3)
y = (2/3)x-26/3
-6= 2.6666+ b (here is where I got confused because of what I got)
-2.6666=-2.6666 (subtract both sides of the equation by the 2.6666)
b=-8.6666
That's approximately correct. However you should be using
fractions, not rounded off decimals. -26/3 is only approximately
equal to -8.6666, and BTW if you were going to round off, it would
have been -8.6667, not -8.6666. But you should have used the
fraction -26/3.
So then I go to plug in the b to the y=mx+b
-6= 2/3(4)+ (-8.6666)
No. After you have found the slope, you don't substitute the point
again as you did to find b. The second time you substitute you leave
x as just the letter x, and y as just the letter y. You don't
substitute anything for them to get the final equation.
So the equation should be
y = (2/3)x + (-26/3)
*It's all supposed to equal -6, but what I get instead is -5.999933333.
Am I doing something wrong?
Yes, you are using a rounded off decimal instead of the fraction. On
top of that, you rounded off incorrectly, and made two typos, once
in typing 2.3 for 2/3 and again typing (4,6) for (4,-6).
Edwin