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kozerog [31]
3 years ago
6

A linear function is graphed below.

Mathematics
2 answers:
AnnyKZ [126]3 years ago
8 0

Answer:

Step-by-step explanation:

find the slope m  by using the slope formula

m = (y2 - y1) / (x2 - x1)

Point1 = ( -1,4)  where it takes the form (x1,y1)

Point2 =(5, -5) where it takes the form (x2,y2)

notice the form is important

m = (-5 -4) / (5 - (-1))

m = -9  /  ( 5 +1 )

m = -9 / 6

m = - 3/2

Evgen [1.6K]3 years ago
4 0

Answer:

-1\frac{1}{2}

Step-by-step explanation:

We have two coordinate points and are asked to find a slope.

When finding slope, we can use the formula listed :

\frac{y^2-y^1}{x^2-x^1}}

To understand what the variables are, you can take this :

(x^1,y^1)

(x^2,y^2)

Substitute the points :

(-1,4)

(5,-5)

Now substitute it into the formula :

\frac{-5-4}{5-(-1)}

\frac{-3}{2}

-1\frac{1}{2}

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The table below represents a linear function in the equation represents a function. table numbers are X: -1,0,1. f(x): -3,0,3. G
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A)
SLOPE OF f(x)
To find the slope of f(x) we pick two points on the function and use the slope formula. Each point can be written (x, f(x) ) so we are given three points in the table. These are: (-1, -3) , (0,0) and (1,3). We can also refer to the points as (x,y). We call one of the points ( x_{1} , y_{1} ) and another ( x_{2} , y_{2} ). It doesn't matter which two points we use, we will always get the same slope. I suggest we use (0,0) as one of the points since zeros are easy to work with.

Let's pick as follows:
( x_{1} , y_{1} )= (0.0)
( x_{2} , y_{2} )= (1.3)

The slope formula is: m= \frac{y_{2} - y_{1} }{ x_{2}- x_{1}  }
We now substitute the values we got from the points to obtain.
m= \frac{3-0}{ 1-0 } = \frac{3}{1}=3

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The equation of a line is y=mx+b where m is the slope and b is the y intercept. Since g(x) is given in this form, the number in front of the x is the slope and the number by itself is the y-intercept.

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The slope of g(x) = 2

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Y-INTERCEPT OF g(x)
From the work in part a we know the y-intercept of g(x) is 2.

Y-INTERCEPT OF f(x)
The y-intercept is the y-coordinate of the point where the line crosses the y-axis. This point will always have an x-coordinate of 0 which is why we need only identify the y-coordinate. Since you are given the point (0,0) which has an x-coordinate of 0 this must be the point where the line crosses the y-axis. Since the point also has a y-coordinate of 0, it's y-intercept is 0

So the function g(x) has the greater y-intercept
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To find the slope of the line, based on the data that we have, we can use this formula:

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