Problem

(37) Find a line that is parallel to $y=x+7$ and passes through the point $(2,4)$.

Answer

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Answer

Final Answer: \(\boxed{y = x + 2}\)

Steps

Step 1 ：Find the slope of the given line $y=x+7$, which is 1.

Step 2 ：Use the point-slope form of a line equation $y - y_1 = m(x - x_1)$, where $m$ is the slope and $(x_1, y_1)$ is the point the line passes through.

Step 3 ：Substitute the slope $m=1$ and the point $(2,4)$ into the point-slope form to get the equation of the parallel line.

Step 4 ：Simplify the equation to get the final answer: $y = x + 2$.

Step 5 ：Final Answer: \(\boxed{y = x + 2}\)

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