key term - Point-Slope Formula

Definition

The point-slope formula is a mathematical equation used to find the equation of a line when given a point on the line and the slope of the line. It allows you to determine the equation of a line in slope-intercept form by using a known point and the slope of the line.

5 Must Know Facts For Your Next Test

1. The point-slope formula is given by the equation $y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is a known point on the line and $m$ is the slope of the line.
2. To use the point-slope formula, you need to have a point $(x_1, y_1)$ on the line and the slope $m$ of the line.
3. The point-slope formula can be rearranged to solve for the $y$-intercept $b$ in the slope-intercept form $y = mx + b$.
4. The point-slope formula is particularly useful when you are given a point on a line and the slope of the line, and you need to find the equation of the line.
5. The point-slope formula can be used to find the equation of a line that passes through a specific point and is parallel or perpendicular to another line.

Review Questions

• Explain the purpose of the point-slope formula and how it is used to find the equation of a line.
  • The point-slope formula is used to find the equation of a line when you are given a point on the line and the slope of the line. It allows you to determine the equation of the line in slope-intercept form by using the known point and slope. The formula is given by $y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is a point on the line and $m$ is the slope of the line. By rearranging this formula, you can solve for the $y$-intercept $b$ in the slope-intercept form $y = mx + b$, which gives you the complete equation of the line.
• Describe how the point-slope formula can be used to find the equation of a line that is parallel or perpendicular to another line.
  • The point-slope formula can be used to find the equation of a line that is parallel or perpendicular to another line. To do this, you need to know a point $(x_1, y_1)$ on the new line and the slope $m$ of the new line. If the new line is parallel to the original line, the slope $m$ of the new line will be the same as the slope of the original line. If the new line is perpendicular to the original line, the slope $m$ of the new line will be the negative reciprocal of the slope of the original line. Once you have the point and the slope, you can use the point-slope formula to determine the equation of the new line.
• Explain how the point-slope formula can be used to find the equation of a line that passes through a specific point and is parallel or perpendicular to another line.
  • The point-slope formula can be used to find the equation of a line that passes through a specific point and is parallel or perpendicular to another line. To do this, you need to know the coordinates of the point $(x_1, y_1)$ and the slope $m$ of the original line. If the new line is parallel to the original line, the slope $m$ of the new line will be the same as the slope of the original line. If the new line is perpendicular to the original line, the slope $m$ of the new line will be the negative reciprocal of the slope of the original line. Once you have the point and the slope, you can use the point-slope formula $y - y_1 = m(x - x_1)$ to determine the equation of the new line. This allows you to find the equation of a line that passes through a specific point and is parallel or perpendicular to another line.

Related terms

Slope:

The slope of a line is a measure of the steepness or incline of the line, and it represents the rate of change between the x and y variables.

Slope-Intercept Form:

The slope-intercept form of a line is the equation of a line written in the form $y = mx + b$, where $m$ is the slope of the line and $b$ is the $y$-intercept.

Linear Equation:

A linear equation is an equation that represents a straight line and can be written in the form $ax + by + c = 0$, where $a$, $b$, and $c$ are constants.