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Readme [11.4K]
4 years ago
15

Which graph represents a linear function of x?

Mathematics
1 answer:
dezoksy [38]4 years ago
6 0

Answer:

Answer 2

Step-by-step explanation:

1 and 3 are not linear or not straight

4 there can't be more then one value for x

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without building the graph, find the coordinates of the point of intersection of the lines given by the equation y=3x-1 and 3x+y
DaniilM [7]
<h2><u>1. Determining the value of x and y:</u></h2>

Given equation(s):

  • y = 3x - 1
  • 3x + y = -7

To determine the point of intersection given by the two equations, it is required to know the x-value and the y-value of both equations. We can solve for the x and y variables through two methods.

<h3 /><h3><u>Method-1: Substitution method</u></h3>

Given value of the y-variable: 3x - 1

Substitute the given value of the y-variable into the second equation to determine the value of the x-variable.

\implies 3x + y = -7

\implies3x + (3x - 1) = -7

\implies3x + 3x - 1 = -7

Combine like terms as needed;

\implies 3x + 3x - 1 = -7

\implies 6x - 1 = -7

Add 1 to both sides of the equation;

\implies 6x - 1 + 1 = -7 + 1

\implies 6x = -6

Divide 6 to both sides of the equation;

\implies \dfrac{6x}{6}  = \dfrac{-6}{6}

\implies x = -1

Now, substitute the value of the x-variable into the expression that is equivalent to the y-variable.

\implies y = 3(-1) - 1

\implies     \ \ = -3 - 1

\implies     = -4

Therefore, the value(s) of the x-variable and the y-variable are;

\boxed{x = -1}   \boxed{y = -4}

<h3 /><h3><u>Method 2: System of equations</u></h3>

Convert the equations into slope intercept form;

\implies\left \{ {{y = 3x - 1} \atop {3x + y = -7}} \right.

\implies \left \{ {{y = 3x - 1} \atop {y = -3x - 7}} \right.

Clearly, we can see that "y" is isolated in both equations. Therefore, we can subtract the second equation from the first equation.

\implies \left \{ {{y = 3x - 1 } \atop {- (y = -3x - 7)}} \right.

\implies \left \{ {{y = 3x - 1} \atop {-y = 3x + 7}} \right.

Now, we can cancel the "y-variable" as y - y is 0 and combine the equations into one equation by adding 3x to 3x and 7 to -1.

\implies\left \{ {{y = 3x - 1} \atop {-y = 3x + 7}} \right.

\implies 0 = (6x) + (6)

\implies0 = 6x + 6

This problem is now an algebraic problem. Isolate "x" to determine its value.

\implies 0 - 6 = 6x + 6 - 6

\implies -6 = 6x

\implies -1 = x

Like done in method 1, substitute the value of x into the first equation to determine the value of y.

\implies y = 3(-1) - 1

\implies y = -3 - 1

\implies y = -4

Therefore, the value(s) of the x-variable and the y-variable are;

\boxed{x = -1}   \boxed{y = -4}

<h2><u>2. Determining the intersection point;</u></h2>

The point on a coordinate plane is expressed as (x, y). Simply substitute the values of x and y to determine the intersection point given by the equations.

⇒ (x, y) ⇒ (-1, -4)

Therefore, the point of intersection is (-1, -4).

<h3>Graph:</h3>

5 0
2 years ago
A company has two manufacturing plants with daily production levels of 5x+17 and 3y-4,respectively.
Troyanec [42]

Complete question :

A company has two manufacturing plants with daily production levels of 5x + 11 items and 2x - 3 items, respectively, where x represents a minimum quantity. The first plant produces how many more items daily than the second plant?

Answer:

3x + 14

Step-by-step explanation:

Given that:

Production level of plant 1 = 5x + 11

Production level of plant 2 = 2x - 3

The first plant produces how many more items daily than the second plant :

Plant 1 production - plant 2 production

(5x + 11) - (2x - 3)

Open the bracket :

5x + 11 - 2x + 3

5x - 2x + 11 + 3

3x + 14

Daily production of plant 1 exceeds that of plant 2 by 3x + 14

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6 3/4 % 5 1/2<br><br> This % means divided by
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Divided by the 5 1/2
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Select all of the potential solution(s) of the equation 2log5x = log54.
tankabanditka [31]

Answer:

-2 and 2

Step-by-step explanation: just did the problem

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3 years ago
4 Ayla s is paid $15 20 per hour for a 34 hour week. April has the same weekly pay but works 38
VashaNatasha [74]

Find Atlas weekly pay by multiplying rate by hours:

15.20 x 34 = 516.80 a week.

Now to find Apri’s rate divide the weekly pay by hours:

516.80 / 38 =$13.60 per hour

5 0
3 years ago
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