25 points! (linear equations and slope) how do i solve for b in y=mx+b with only coordinates? provide a good explanation, along with an answer and another explanation for the example! here's the example: (i've changed numbers from the original question) what is the slope-intercept form of the equation of the line that contains the points (4, 2) and (8, -3) ?

You could do point-slope, but if you want to do it in slope-intercept:

y = mx + b

Using your example, we can start by finding the slope, which is . Plug in this slope and one of the points into the slope-intercept equation:

2 = (4) + b

Multiplying the slope, which has a denominator of 4, by 4 will just cancel out the denominator, giving you -5:

2 = -5 + b

Finish by adding 5 to both sides:

7 = b

Therefore, b = 7.

Hope this helps! :)

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb