Mathematics, 14.11.2019 10:31 ejuarez2020

Which graph represents the line
10x + 5y = 20?

Which graph represents the line 10x + 5y = 20?

Answers: 1

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Answer from: UaRemomGAY

Option 1.

Step-by-step explanation:

The given equation of the line is 10x + 5y = 20

Now we will convert this equation into y-intercept form

10x + 5y = 20

5y = 20 - 10x

y = $\frac{1}{5}$ (20 _ 10x)

= -2x + 4

y-intercept of the line is 4 which gives us hint that graph (1) or (2) may be the correct option.

Since slope is (-2)

So from graph (1) slope of the line passing through (0,4) and (-2,0) = $\frac{4.0}{0+2}$ = 2

Therefore, graph A is not the answer.

For graph (2) slope of the graphed line passing through (0,4) and (2,0) = $\frac{4-0}{0-2}$ = (-2)

So graph (2) is representing the line y = -2x +4

Option 1. is the answer.

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

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2 = -20

divide by -2 on each side

-2x^2 /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

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Which graph represents the line
10x + 5y = 20?
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