Find the equation of the line with a y-intercept of -3 and a x-intercept of -4.5

So with intercepts, we know that one of the coordinates is 0 - that is because the line intercepts the axis at this point.

When we have a y-intercept of -3, it is written as (0,-3)

And when we have an x-intercept of -4.5, we write it as (-4.5,0)

So now we have our two points - let's find the slope using the equation:

--->

If we convert -4.5 to an improper fraction, we get:

So then we go back and simplify:

So now we have our slope: . Then we can write the equation:

Let's use the point (0,-3) to solve for b:

So now we can write the equation:

This is the equation of the line with points (0,-3) and (-4.5,0).

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

a

step-by-step explanation: