Mathematics, 15.07.2019 21:30 fryday3111

Which table represents a linear function?

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For it to be a linear equation, the same difference in x must produce the same difference in y always.

Choice A.
difference in x: 2 - 1 = 1
difference in y: -6 - (-2) = -4

difference in x: 3 - 2 = 1
difference in y: -2 - (-6) = 4

A difference of 1 in x gave a difference of -4 in y and another difference of 1 in x gave a difference of 4 in y.
This is not linear.

Choice B.
difference in x: 2 - 1 = 1
difference in y: -5 - (-2) = -3

difference in x: 3 - 2 = 1
difference in y: -9 - (-5) = -4

A difference of 1 in x gave a difference of -3 in y and another difference of 1 in x gave a difference of -4 in y.
This is not linear.

Choice C.
difference in x: 2 - 1 = 1
difference in y: -10 - (-2) = -8

difference in x: 3 - 2 = 1
difference in y: -18 - (-10) = -8

Do the other differences. All differences in y are -8 corresponding to a difference in x of -1.

This is linear.

Choice D.
The differences in y vary. It is not linear.

Choice C is linear.

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

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

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is

$y\leq -x+4$

similarly, check the second related equation.

$3(1)=0$

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

$3y> x$

15 points write a system of inequalities to represent the shaded portion of the graph

Answer from: Quest

The answer to the question is d

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