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Find the equation for the function described below. (Let x be the independent variable and y be the dependent variable.) The linear function whose graph is parallel to y = 5x + 2 and passes through the point (−2, 2)

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The key to solving this problem is to know that parallel lines have the same slope. So, the equation of the line we're looking for can be written as y = 5x + b, because it's the same slope, 5, as the line y = 5x + 2.

The 'b' represents the y-intercept of the line, and it's the only thing we don't know yet.

To find 'b', we can use the fact that the line passes through the point (-2, 2). This means that when x = -2, y = 2. We substitute these values into the equation, giving us 2 = 5 * -2 + b.

Solve the equation for b, which is:
b = 2 - 5 * -2.
Remember to multiply first (PMDAS/BODMAS rule), giving us b = 2 + 10,
Therefore, b = 12.

In conclusion, the equation of the line parallel to y = 5x + 2, which passes through the point (-2, 2), is y = 5x + 12.

User Ji Fang
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