Write the equation of the line through the points (1, -1) and (3, 5).

Step 1: Calculate the slope

The slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula for the change in $y$ divided by the change in $x$. We will use the given points $(1, -1)$ and $(3, 5)$ to calculate the slope.

Step 2: Substitute coordinates to find slope

Substitute the coordinates of the given points $(x_1, y_1) = (1, -1)$ and $(x_2, y_2) = (3, 5)$ into the slope formula. This gives us a slope of 3.

Step 3: Use the point-slope form

Now that we have the slope, we can use the point-slope form of a linear equation. This form requires the slope $m$ and one point $(x_1, y_1)$ on the line.

Step 4: Substitute slope and a point

Substitute the calculated slope $m=3$ and one of the given points, for example $(1, -1)$, into the point-slope form. This will allow us to simplify the equation into the standard slope-intercept form.

Step 5: Simplify to slope-intercept form

Simplify the equation by distributing the slope and isolating $y$ to get the equation in the slope-intercept form, $y = mx + c$.

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