# Climbing Alpine Peaks

- Author:
- Jaime Dianzon, Steve Phelps

- Topic:
- Algebra, Linear Equations

## Is Alpine climbing dangerous?

## OBJECTIVE: To learn how to graph a line on the Cartesian plane using a point and the slope

In a previous lesson, you learned how to graph a line on the Cartesian plane using the

*slope*and the*y-intercept*.*Riding the Berms*: https://www.geogebra.org/m/nkwt8g3y In this lesson, you'll be introduced to yet another form of the equation of a line—the*POINT-SLOPE FORM, (y - y₁) = m(x - x₁)*where*(x₁, y₁)*are the coordinates of a*point*and*m*is the*slope*. The process of graphing a line using a*point*and the*slope*is very similar to graphing a line using the*slope*and the*y-intercept*. In fact, the*y-intercept*is just another*point*, but it is a*special point*in the sense that it always lies on the y-axis. Interact with the applet below to learn how to graph a line using a*point*(*any**point)*and the*slope*.## INSTRUCTIONS:

1. Move point A to the position indicated by (x₁, y₁) in the linear equation.
2. Use

*rise/run*to locate point B on the line. 3. If your graph is correct, the expression will appear. Otherwise, you'll have to try again. 4. Click "Generate New Line" to come up with another problem. 5. Repeat as many times as needed to master the concept.The applet below shows a variation of the POINT-SLOPE FORM

*, y = m(x - x₁) +*where*y₁**are the coordinates of a**(x₁, y₁)**and**point**is the**m**Interact with the applet to learn how to graph a line using a**slope*.*and the**point*(*any**point)**slope*.## INSTRUCTIONS:

1. Move point A to the position indicated by (x₁, y₁) in the linear equation.
2. Use

*rise/run*to locate point B on the line. 3. If your graph is correct, the expression will appear. Otherwise, you'll have to try again. 4. Click "Generate New Line" to come up with another problem. 5. Repeat as many times as needed to master the concept.QUESTION: In getting the coordinates (x₁, y₁) in the second formula, what do you observe about the sign of *y₁*?

## TODAY you learned how to graph a line on the Cartesian plane using a point and the slope.

In future lessons, you'll learn how to work out the equations of a line from the graphs. Did you ENJOY your lesson today?