Questions: Write an equation of the line passing through the points (3,10) and (-1,-14).

Transcript text: Write an equation of the line passing through the points $(3,10)$ and $(-1,-14)$.

Solution

Solution Steps

Step 1: Determine the Slope

To find the equation of the line passing through two points, we first need to determine the slope $ m $ of the line. The formula for the slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Substituting the given points $(3, 10)$ and $(-1, -14)$:

\[ m = \frac{-14 - 10}{-1 - 3} = \frac{-24}{-4} = 6 \]

Step 2: Use the Point-Slope Form

With the slope $ m = 6 $ and one of the points, say $(3, 10)$, we can use the point-slope form of the equation of a line:

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

Substituting the values:

\[ y - 10 = 6(x - 3) \]

Step 3: Simplify to Slope-Intercept Form

Now, simplify the equation to get it into the slope-intercept form $ y = mx + b $:

\[ y - 10 = 6x - 18 \]

Add 10 to both sides:

\[ y = 6x - 18 + 10 \]

\[ y = 6x - 8 \]

Final Answer

The equation of the line passing through the points $(3, 10)$ and $(-1, -14)$ is:

\[ \boxed{y = 6x - 8} \]

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