Question

What do the following two equations represent? y = -x + 5; 5x + 5y = 20 Choose 1 answer: A. The same line B. Distinct parallel lines C. Perpendicular lines D. Intersecting, but not perpendicular lines

Answer 1

The two equations y = -x + 5 and 5x + 5y = 20 represent the same line.

Step-by-step explanation:

The first equation, y = -x + 5, represents a linear equation in slope-intercept form. The slope of -1 indicates that for every unit increase in x, y will decrease by 1. The y-intercept of 5 indicates that the line intersects the y-axis at (0, 5).

The second equation, 5x + 5y = 20, represents a linear equation in standard form. To find the slope-intercept form, we can rewrite the equation as y = -x + 4, by dividing both sides by 5. Comparing it with the first equation, we can see that the two equations are equivalent. Therefore, the two equations represent the same line.

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