Questions: Find an equation of the line that satisfies the given conditions. Through (4,9); parallel to the line passing through (5,7) and (1,3)

Transcript text: Find an equation of the line that satisfies the given conditions. Through $(4,9)$; parallel to the line passing through $(5,7)$ and $(1,3)$ $\square$

Solution

Solution Steps

Step 1: Calculate the slope of the line

The slope $m$ is calculated using the formula $m = (y_3 - y_2) / (x_3 - x_2)$ with points $(5, 7)$ and $(1, 3)$. Substituting the given points, $m = (3 - 7) / (1 - 5) = 1$.

Step 2: Use the point-slope form of the line equation

The point-slope form of the line equation is $y - y_1 = m(x - x_1)$, where $m$ is the slope and $(x_1, y_1)$ is the point through which the line passes. Substituting $m = 1$ and the point $(4, 9)$, we get $y - 9 = 1(x - 4)$.

Final Answer

The equation of the line in slope-intercept form is $y = 1.0x + 5$.

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