Questions: Find an equation for the line that passes through the points (-6,-1) and (4,3).

Transcript text: Find an equation for the line that passes through the points $(-6,-1)$ and $(4,3)$.

Solution

Solution Steps

To find the equation of a line passing through two given points, we first calculate the slope using the formula $ m = \frac{y_2 - y_1}{x_2 - x_1} $. Then, we use the point-slope form of the equation of a line, $ y - y_1 = m(x - x_1) $, to find the equation by substituting one of the points and the slope.

Step 1: Calculate the Slope

To find the slope $ m $ of the line passing through the points $(-6, -1)$ and $(4, 3)$, we use the formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - (-1)}{4 - (-6)} = \frac{4}{10} = 0.4 \]

Step 2: Use Point-Slope Form

Next, we apply the point-slope form of the equation of a line, which is given by:

\[ y - y_1 = m(x - x_1) \]

Substituting one of the points, say $(-6, -1)$, and the calculated slope $ m = 0.4 $:

\[ y - (-1) = 0.4(x - (-6)) \]

Step 3: Rearrange to Slope-Intercept Form

Now, we rearrange the equation to the slope-intercept form $ y = mx + b $:

\[ y + 1 = 0.4(x + 6) \]

Expanding this gives: