1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
nexus9112 [7]
3 years ago
13

What is true of the graph of two lines 3y-8=-5x and 6y=-10x+16

Mathematics
1 answer:
Murljashka [212]3 years ago
6 0

Answer:

Both lines are equal (they are the same)

<em></em>

Step-by-step explanation:

Given

3y - 8 = -5x

6y = -10x + 16

Required

What is true about graph of both lines

<em>Questions like this are better solved when there's option(s) to select from. However, some of the properties of line equation that I'll consider are to check  if both lines are either parallel or perpendicular</em>

<em />

To do this,

The first thing to do is to calculate the slope of both lines

3y - 8 = -5x

Add 8 to both sides

3y - 8 + 8 = -5x + 8

3y = -5x + 8

Divide both sided by 3

\frac{3y}{3} = -\frac{5x}{3} + \frac{8}{3}

y = -\frac{5x}{3} + \frac{8}{3}

The slope of the line is the coefficient of x;

Slope = -\frac{5}{3}

Solve for the y intercept; <em>Let x = 0</em>

y = -\frac{5 * 0}{3} + \frac{8}{3}

y = 0 + \frac{8}{3}

y = \frac{8}{3}

Solve for the x intercept; <em>Let y = 0</em>

0 = -\frac{5x}{3} + \frac{8}{3}

Subtract \frac{8}{3} from both sides

0 - \frac{8}{3} = -\frac{5x}{3} + \frac{8}{3} - \frac{8}{3}

- \frac{8}{3} = -\frac{5x}{3}

Subtract both sides by -\frac{3}{5}

-\frac{3}{5}*- \frac{8}{3} = -\frac{5x}{3} * -\frac{3}{5}

-\frac{3}{5}*- \frac{8}{3} = x

\frac{3}{5} * \frac{8}{3} = x

\frac{8}{5} = x

x = \frac{8}{5}

------------------------------------------------------------------------------------------------------

6y = -10x + 16

Divide both sides by 6

\frac{6y}{6} = -\frac{10x}{6} + \frac{16}{6}

y = -\frac{10x}{6} + \frac{16}{6}

Simplify fractions to lowest term

y = -\frac{5x}{3} + \frac{8}{3}

The slope of the line is the coefficient of x;

Slope = -\frac{5}{3}

Solve for the y intercept; <em>Let x = 0</em>

y = -\frac{5 * 0}{3} + \frac{8}{3}

y = 0 + \frac{8}{3}

y = \frac{8}{3}

Solve for the x intercept; <em>Let y = 0</em>

0 = -\frac{5x}{3} + \frac{8}{3}

Subtract \frac{8}{3} from both sides

0 - \frac{8}{3} = -\frac{5x}{3} + \frac{8}{3} - \frac{8}{3}

- \frac{8}{3} = -\frac{5x}{3}

Subtract both sides by -\frac{3}{5}

-\frac{3}{5}*- \frac{8}{3} = -\frac{5x}{3} * -\frac{3}{5}

-\frac{3}{5}*- \frac{8}{3} = x

\frac{3}{5} * \frac{8}{3} = x

\frac{8}{5} = x

x = \frac{8}{5}

-------------------------------------------------------------------------------------------------------

By comparing the slope, x intercept and y intercept of both lines;

It'll be observed that they have the same slope, x intercept and y intercept

<em>This implies that both lines are equal; in other words, they are the same.</em>

You might be interested in
What is the equation of the line which has a gradient of 2 and passes through the point (1,4)
timofeeve [1]

Answer:

Y= 2x+2

Step-by-step explanation:

line equation is y=mx +c


m is the gradient = 2

We are given an x and y value

X= 1
y= 4


substitute that into the equation:

4= 2(1) +c

2=c


Put all the equation together:

Y= 2x+2

5 0
2 years ago
Two friends share 7 cookies equally .How many cookies does each friend get
algol13

Answer:

they would get 3 1/2

Step-by-step explanation:

because if there's two friends and seven cookies one friend we get three and the other one will get three and they could split the other cookie in half so that each Friend can have three cookies and a half if they split

7 0
3 years ago
B) Find the value of 3^-3 x 10^-3
DerKrebs [107]

Answer:

no

Step-by-step explanation:

8 0
4 years ago
Evaluating expressions k3+j
mrs_skeptik [129]
The answer is 3k+j since 3 cannot be multiplied after k.
3 0
3 years ago
What is the correct evaluation of 4x2 + 4x - 2y2 +3y, when x is equal to -2 and y is equal to 3?
____ [38]

Answer:

-1

Step-by-step explanation:

This all comes down to the substitution. I am assuming that (4x2) is meant to be 4x^2 so I will solve as that.

4(-2)^2 = 4(4) = 16

4(-2) = - 8    

-2(3)^2 = -2(9) = -18

3(3) = 9

16-8-18+9= -1

7 0
2 years ago
Other questions:
  • Choose the best translation of the English phrase.
    5·2 answers
  • an airline ramp with a base of 50 makes an angle of 27 with the ground. find the distance a person will walk on a ramp round to
    8·1 answer
  • Josh is preparing for an exam by completing practice tests that have different numbers of questions. For each practice test, he
    6·2 answers
  • A water storage tank is in the shape of a hemisphere (half a sphere) If the radius is 15 ft, approximate the volume of the tank
    13·1 answer
  • Does the rule y=6x^7 represent an exponential function
    14·2 answers
  • Help plz ASAP Find the value of x
    7·1 answer
  • I will mark you Brainliest if your response is correct. Also, I'm offering 20 points.
    5·2 answers
  • Find the roots of the following factored quadratic equation.<br> y= (2x-9) (7x-4)
    8·1 answer
  • What’s the gcf of 2x+6?
    9·1 answer
  • Hey guys I need some help with this question so if anyone could help that would be great THANK YOU!!
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!