All categories

3 years ago

Match the correct y=mx+b equation to the graph: pls show work/explanation!

Mathematics

1 answer:

Basile [38]3 years ago

5 0

Answer:

$y=-3x+2$

$\boxed{m=-3,\ b=2}$

Step-by-step explanation:

Equation of a line

To define the equation of a line, we only need two points through which it passes. The graph shows two clear points to choose: (0,2) and (1,-1)

Set up the equation of the line by using the formula

$\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

$\displaystyle y-2=\frac{-1-2}{1-0}(x-0)$

Operating

$y-2=-3x$

Rearranging

$y=-3x+2$

$\boxed{m=-3,\ b=2}$

You might be interested in

For f(x) = 3x - 1 and g(x) = x+2, find (f – g)(x).

kobusy [5.1K]

Well, I bet you want your answer right away! So here it is.

Given f (x) = 3x + 2 and g(x) = 4 – 5x, find (f + g)(x), (f – g)(x), (f × g)(x), and (f / g)(x).

To find the answers, all I have to do is apply the operations (plus, minus, times, and divide) that they tell me to, in the order that they tell me to.

(f + g)(x) = f (x) + g(x)

= [3x + 2] + [4 – 5x]

= 3x + 2 + 4 – 5x

= 3x – 5x + 2 + 4

= –2x + 6

(f – g)(x) = f (x) – g(x)

= [3x + 2] – [4 – 5x]

= 3x + 2 – 4 + 5x

= 3x + 5x + 2 – 4

= 8x – 2

(f × g)(x) = [f (x)][g(x)]

= (3x + 2)(4 – 5x)

= 12x + 8 – 15x2 – 10x

= –15x2 + 2x + 8

\left(\small{\dfrac{f}{g}}\right)(x) = \small{\dfrac{f(x)}{g(x)}}(gf)(x)=g(x)f(x)= \small{\dfrac{3x+2}{4-5x}}=4−5x3x+2

My answer is the neat listing of each of my results, clearly labelled as to which is which.

( f + g ) (x) = –2x + 6

( f – g ) (x) = 8x – 2

( f × g ) (x) = –15x2 + 2x + 8

\mathbf{\color{purple}{ \left(\small{\dfrac{\mathit{f}}{\mathit{g}}}\right)(\mathit{x}) = \small{\dfrac{3\mathit{x} + 2}{4 - 5\mathit{x}}} }}(gf)(x)=4−5x3x+2

Hope I helped! :) If I did not help that's okay.

-Duolingo

7 0

3 years ago

LAST QUESTION PLEASE HELP IF YOU CAN FOR 11 POINTS AND BRAINLIEST + THANK YOU

jekas [21]

Answer:

see attachment

Step-by-step explanation:

The y-intercept is +4 for both lines, so only the third selection is appropriate. The lines appear to have a slope of magnitude less than 1, so ±1/2 seems about right.

(We expect at least one of the inequality symbols to include the "or equal to" case so there is no hole at x=0. Alas, it seems the third answer choice doesn't do that.)