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nexus9112 [7]
2 years ago
13

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

Mathematics
1 answer:
Murljashka [212]2 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>

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Step-by-step explanation:

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On a coordinate plane, a line goes through (negative 12, negative 2) and (0, negative 4). A point is at (0, 6).
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Point (-12 , 8) is on the line that passes through (0, 6) and is parallel to the given line ⇒ 1st

Step-by-step explanation:

Parallel lines have:

  • Same slopes
  • Different y-intercepts

The formula of the slope of a line which passes through points (x_{1},y_{1}) and (x_{1},y_{1}) is m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

∵ The given line passes through points (-12 , -2) and (0 , -4)

∴ x_{1} = -12 , x_{2} = 0

∴ y_{1} = -2 , y_{2} = -4

- Use the formula of the slope above to find the slope of the given line

∵ m=\frac{-4-(-2)}{0-(-12)}=\frac{-4+2}{12}=\frac{-2}{12}=\frac{-1}{6}

∴ The slope of the given line is \frac{-1}{6}

∵ The two lines are parallel

∴ Their slopes are equal

∴ The slope of the parallel line = \frac{-1}{6}

∵ The parallel line passes through point (0 , 6)

- The form of the linear equation is y = mx + b, where m is the slope

  and b is the y-intercept (y when x = 0)

∵ m = \frac{-1}{6} and b = 6

∴ The equation of the parallel line is y = \frac{-1}{6} x + 6

Let us check which point is on the line by substitute the x in the equation by the x-coordinate of each point to find y, if y is equal the y-coordinate of the point, then the point is on the line

Point (-12 , 8)

∵ x = -12 and y = 8

∵ y = \frac{-1}{6} (-12) + 6

∴ y = 2 + 6 = 8

- The value of y is equal the y-coordinate of the point

∴ Point (-12 , 8) is on the line

Point (-12 , 8) is on the line that passes through (0, 6) and is parallel to the given line

Learn more:

You can learn more about the equations of parallel lines in brainly.com/question/9527422

#LearnwithBrainly

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