Y - y1 = m(x - x1)

Definition

The equation y - y1 = m(x - x1) is a linear equation that represents the equation of a line. It describes the relationship between the coordinates (x, y) and (x1, y1) on a line, where m is the slope of the line.

5 Must Know Facts For Your Next Test

1. The equation y - y1 = m(x - x1) is used to find the equation of a line when given a point (x1, y1) and the slope, m.
2. This form of the linear equation is known as the point-slope form, as it relates the coordinates of a point on the line to the slope.
3. The point-slope form can be rearranged to the slope-intercept form, y = mx + b, by solving for y.
4. The point-slope form is useful when you know a point on the line and the slope, but don't know the y-intercept.
5. Understanding the point-slope form is crucial for finding the equation of a line in various problem-solving scenarios.

Review Questions

• Explain how the point-slope form, y - y1 = m(x - x1), can be used to find the equation of a line.
  • The point-slope form, y - y1 = m(x - x1), is used to find the equation of a line when you know a point (x1, y1) on the line and the slope, m. By rearranging the equation, you can solve for the y-intercept, b, to obtain the slope-intercept form, y = mx + b, which fully describes the equation of the line. This form is particularly useful when you don't know the y-intercept but have a known point and the slope.
• Describe how the point-slope form, y - y1 = m(x - x1), is related to the slope-intercept form, y = mx + b, of a linear equation.
  • The point-slope form, y - y1 = m(x - x1), and the slope-intercept form, y = mx + b, are both representations of a linear equation, but they emphasize different aspects of the line. The point-slope form focuses on a known point (x1, y1) and the slope, m, while the slope-intercept form highlights the slope, m, and the y-intercept, b. The two forms are related, as the point-slope form can be rearranged to obtain the slope-intercept form by solving for y. Understanding the connection between these forms is crucial for selecting the appropriate representation based on the given information about the line.
• Analyze how the point-slope form, y - y1 = m(x - x1), can be used to determine the equation of a line that passes through a specific point and is parallel or perpendicular to another line.
  • The point-slope form, y - y1 = m(x - x1), can be used to determine the equation of a line that passes through a specific point (x1, y1) and is parallel or perpendicular to another line with a known slope, m. If the new line is parallel to the original line, the slope of the new line will be the same as the original slope, m. If the new line is perpendicular to the original line, the slope of the new line will be the negative reciprocal of the original slope, -1/m. By substituting the known point (x1, y1) and the appropriate slope value into the point-slope form, you can find the equation of the new line that satisfies the given conditions.

Related terms

Slope: The slope, m, represents the rate of change or steepness of a line, calculated as the change in y-coordinate divided by the change in x-coordinate between two points.

Point-Slope Form: The point-slope form of a linear equation is y - y1 = m(x - x1), where (x1, y1) is a known point on the line and m is the slope.

Slope-Intercept Form: The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.