Mathematics, 22.12.2020 01:20 jholland03

Select ALL of the following points that lie on the graph of f (x) = 7 - 3x

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Answer from: smithcj0505

(-1, 10)

(2, 1)

(0, 7)

Step-by-step explanation:

Any points, that makes the equation of the function, f(x) = 7 - 3x, true, is a point that lies on the graph of the function.

Let's check each of the options.

Option 1: (-2, 1).

Plug in x = -2, f(x) = 1 into f(x) = 7 - 3x

1 = 7 - 3(-2)

1 = 7 + 6

1 = 13 (this is not true)

Thus, (-2, 1) is not a point that lies on the graph of the function.

Option 2: (-1, 10).

Plug in x = -1, f(x) = 10 into f(x) = 7 - 3x

10 = 7 - 3(-1)

10 = 7 + 3

10 = 10 (this is true)

Thus, (-1, 10) is a point that lies on the graph of the function.

Option 3: (2, 1).

Plug in x = 2, f(x) = 1 into f(x) = 7 - 3x

1 = 7 - 3(2)

1 = 7 - 6

1 = 1 (this is true)

Thus, (2, 1) is a point that lies on the graph of the function.

Option 4: (0, 7).

Plug in x = 0, f(x) = 7 into f(x) = 7 - 3x

7 = 7 - 3(0)

7 = 7 - 0

7 = 7 (this is true)

Thus, (0, 7) is a point that lies on the graph of the function.

Option 5: (1, 5).

Plug in x = 1, f(x) = 5 into f(x) = 7 - 3x

5 = 7 - 3(1)

5 = 7 - 3

5 = 4 (this is not true)

Thus, (1, 5) is NOT a point that lies on the graph of the function.

Answer from: Quest

step-by-step explanation:

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

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Select ALL of the following points that lie on the graph of f (x) = 7 - 3x
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