Point-Slope Form

In mathematics, the point-slope form of a linear equation is useful for writing the equation of a line when you know the slope and a point on the line. The point-slope form is expressed as:

$y - y_{1} = m(x - x_{1})$

Where:

• $(x_{1}, y_{1})$ is a point on the line
• $m$ is the slope of the line

Worked Example

Let's find the equation of a line with a slope of $2$ that passes through the point $(3, 4)$.

1. Identify the slope and point:

   • Slope $m = 2$
   • Point $(x_{1}, y_{1}) = (3, 4)$

2. Substitute the values into the point-slope formula: $y - 4 = 2(x - 3)$

3. Distribute the slope on the right side: $y - 4 = 2x - 6$

4. Add $4$ to both sides to solve for $y$: $y = 2x - 2$

Thus, the equation of the line in slope-intercept form is $y = 2x - 2$.

Key Questions

• What is the point-slope form of a line?
• How do you convert from point-slope form to slope-intercept form?
• Given a slope of $-3$ and a point $(1, 2)$, what is the point-slope equation?
• How can you identify the slope and point from an equation in slope-intercept form?
• Why is the point-slope form useful in graphing linear equations?

Keywords

• Point-Slope Form
• Linear Equation
• Slope
• Coordinate Plane
• Equation of a Line