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The lines represented by the equations y=x+5 and 2y-2x=10 are

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The equations representing the lines, y=x+5 and 2y-2x=10, have the same slope, therefore the lines are parallel.

Recall:

  • Two lines that are parallel will have the same slope value.
  • Two lines that are perpendicular to each other will have slopes that are negative reciprocal of each other.
  • Equation representing a line in slope-intercept form is: y = mx + b, where m is the slope.

Given:

y = x + 5

2y - 2x = 10

The slope of y = x + 5 is 1.

Rewrite 2y - 2x = 10 in slope-intercept form to determine its slope.

2y - 2x = 10

2y = 2x + 10

  • Divide both sides by 2

y = x + 5

Thus, the slope of y = x + 5 (2y - 2x = 10) is also 1.

The equations representing the lines, y=x+5 and 2y-2x=10, have the same slope, therefore the lines are parallel.

Learn more about slope of parallel lines on:

https://brainly.com/question/10790818

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