Questions: Find an equation for the line that passes through the points (5,-3) and (-1,5).

Transcript text: Find an equation for the line that passes through the points $(5,-3)$ and $(-1,5)$.

Solution

Solution Steps

Step 1: Calculate the slope (m)

To find the slope of the line that passes through the points $(5, -3)$ and $(-1, 5)$, we use the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$. Substituting the given values, we get $m = \frac{5 + 3}{-1 - 5} = -1.33$.

Step 2: Find the y-intercept (b)

With the slope calculated, we can find the y-intercept (b) using the point-slope form equation $y - y_1 = m(x - x_1)$ and rearranging it to the slope-intercept form $y = mx + b$. Substituting $m = -1.33$ and one of the points $(5, -3)$, we solve for $b$: $b = y_1 - m \cdot x_1 = -3 - (-1.33) \cdot 5 = 3.67$.

Final Answer:

The equation of the line that passes through the points $(5, -3)$ and $(-1, 5)$ is $y = -1.33x + 3.67$.

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