Mathematics, 25.09.2019 22:00 hii2857

a table contains the ordered pairs (3, 42.25) and (5, 50.75). if the relationship in the table is linear, explain how to find the initial value.

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Answer from: tabbic

The initial value is 29.5

Step-by-step explanation:

we know that

The linear equation in slope intercept form is equal to

y=mx+b

where

m is the slope

b is the y-intercept ( also called initial value)

we have the points

(3,42.25) and (5,50.75)

Find the slope m

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{50.75-42.25}{5-3}$

$m=\frac{8.5}{2}$

m=4.25

substitute in the equation

y=4.25x+b

Find the value of b

with the point (3,42.25) ( or the other given point)

substitute the value of x and the value of y in the equation and solve for b

42.25=4.25(3)+b

42.25=12.75+b

b=42.25-12.75

b=29.5

substitute

The linear equation is

y=4.25x+29.5

The initial value is the y-intercept (value of y when the value of x is equal to zero)

For x=0

y=4.25(0)+29.5

y=29.5

Therefore

The initial value is 29.5

Answer from: Quest

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step-by-step explanation:

Answer from: Quest

$y> \frac{1}{3}x$ and y≤ -x +4 .

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be = $\frac{1-0}{3-0} = \frac{1}{3}$ .

y-intercept of dotted line is y=0 only.

plugging slope m= $\frac{1}{3}$ and b=0 in slope-intercept form y=mx+b, we get

$y=\frac{1}{3}x$ .

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

$y> \frac{1}{3}x$ .

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be = $\frac{4-1}{0-3} = \frac{3}{-3}=-1$ .

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

y≤ -x +4 .
Write a system of inequalities to represent the shaded portion of the graph.

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a table contains the ordered pairs (3, 42.25) and (5, 50.75). if the relationship in the table is li...

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