How is the point-slope formula used after finding the slope?

Conditions

• The slope $m$ of the line is already known.
• At least one point $(x_1, y_1)$ that lies on the line is known.
• The goal is to find the equation of the line.

Reasoning, step by step

1. Write down the point-slope formula: $y - y_1 = m(x - x_1)$.
2. Substitute the known slope $m$ into the equation.
3. Substitute the x and y coordinates of the chosen point into $x_1$ and $y_1$.
4. Simplify the equation by distributing the slope and combining like terms.
5. Isolate y to convert the equation into slope-intercept form.

Example

The video states: "Now that we have the slope, we can use the point slope formula. All we need is a point and a slope." With $m=1$ and point $(-1, -3)$, it becomes $y - (-3) = 1(x - (-1))$, which simplifies to $y = x - 2$.

Common misconceptions

• Using a point that is not on the line.
• Forgetting to distribute the slope $m$ to both terms inside the parentheses.
• Thinking that a specific point must be used; any point on the line will yield the same final equation.

Watch the explanation

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