Write an equation that describes the line that passes through (2, 2) and (0, -3).

Mathematics

1 answer:

gtnhenbr [62]4 years ago

5 0

Answer:

f(x) = $\frac{5}{2}$ x

Step-by-step explanation:

The first thing we need to find is the slope of the line able to pass through the given two points. Right now we have y = mx + b (linear function equation) and we need to find m.

Using the slope formula or $m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}$ and plugging in the given points' x and y values:

$\frac{-3-2}{0-2}$ = $\frac{-5}{-2}$ = $\frac{5}{2}$

The slope of the line is that for every 5 units the line goes upwards, it goes 2 units to the right.

Our equation is now y = $\frac{5}{2}$ x + b. If you were in need of it, b gives the line's y-intercept, the place where it hits the y-axis. In this case you do not need b because the only specified conditions in the problem are the units the line hits.

Our final equation is:

f(x) = $\frac{5}{2}$ x

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HELP ME MATH ILL GIVE YOU BRAINLIEST

s344n2d4d5 [400]

Answer:

zeros: x = -3, -1, +2.
end behavior: as x approaches -∞, f(x) approaches -∞.

Step-by-step explanation:

I like to use a graphing calculator for finding the zeros of higher order polynomials. The attachment shows them to be at x = -3, -1, +2.

The zeros can also be found by trial and error, trying the choices offered by the rational root theorem: ±1, ±2, ±3, ±6. It is easiest to try ±1. Doing so shows that -1 is a root, and the residual quadratic is ...

x² +x -6

which factors as (x -2)(x +3), so telling you the remaining roots are -3 and +2.

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For any odd-degree polynomial with a positive leading coefficient, the sign of the function will match the sign of x when the magnitude of x gets large. Thus as x approaches negative infinity, so does f(x).