What is the standard form of the line that has x-intercept 6 and y-intercept -2

Mathematics

1 answer:

alisha [4.7K]2 years ago

4 0

Answer:

Step-by-step explanation:

The Standard Form of an equation of a line:

$Ax+By=C$

We have the x-intercept and the y-intercept

x-intercept is for y = 0

y-intercept is for x = 0

Therefore we have two points: (6, 0) and (0, -2).

The slope-intercept form of an equation of a line:

$y=mx+b$

m - slope

b - y-intercept

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

Calculate the slope:

$m=\dfrac{-2-0}{0-6}=\dfrac{-2}{-6}=\dfrac{1}{3}$

Put it and the value of y-intercept b = -2 to the equation of a line:

$y=\dfrac{1}{3}x-2$

Convert to the standard form:

$y=\dfrac{1}{3}x-2$ multiply both sides by (-3)

$-3y=-x+6$ add x to both sides

$x-3y=6$

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HELP.... please??????????????

Nostrana [21]

Answers:

Functions

y = -x+11
y = 2x^2-6x+4
y = -7

Not functions

x = 3
x^2+y^2 = 81
y^2 = -5x-12

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Explanation:

A function is possible if and only if any given x input leads to exactly one y output.

For something like x^2+y^2 = 81, we can see that x = 0 leads to either y = 9 or y = -9. So this would not be a function. We would need x to pair with only y value to have it be a function.

We have the same thing going on with y^2 = -5x-12 as well.

For anything of the form x = k, where k is any real number, this is also not a function. We have one single input only and it leads to infinitely many outputs. So in a sense, this is even worse compared to the other examples.

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In summary, we have these three non-functions: