Learn on PengiBig Ideas Math, Algebra 1Chapter 3: Graphing Linear Functions

Lesson 2: Linear Functions

Property The slope intercept form for a linear equation is $y = mx + b$, where $m$ is the slope of the line and the point $(0, b)$ is the y intercept.

Section 1

The Core Formula: Slope and Y-Intercept

Property

The slope-intercept form for a linear equation is $y = mx + b$ , where $m$ is the slope of the line and the point $(0, b)$ is the y-intercept.

The slope formula between two points $(x_1, y_1)$ and $(x_2, y_2)$ is $m = \frac{y_2 - y_1}{x_2 - x_1}$ .

This formula calculates the ratio of the change in the y-coordinates (rise) to the change in the x-coordinates (run).

Section 2

Lines Have Constant Slope

Property

The slope of a line is constant: no matter which two points you pick to compute the slope, you will always get the same value.

Because $m$ is constant for a given line, we can use the formula $m = \frac{\Delta y}{\Delta x}$ to find $\Delta y$ when we know $\Delta x$ , or to find $\Delta x$ when we know $\Delta y$ .

We can also tell whether a collection of data points lies on a straight line by computing slopes between them.

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

The Core Formula: Slope and Y-Intercept

Property

The slope-intercept form for a linear equation is $y = mx + b$ , where $m$ is the slope of the line and the point $(0, b)$ is the y-intercept.

The slope formula between two points $(x_1, y_1)$ and $(x_2, y_2)$ is $m = \frac{y_2 - y_1}{x_2 - x_1}$ .

This formula calculates the ratio of the change in the y-coordinates (rise) to the change in the x-coordinates (run).

Section 2

Lines Have Constant Slope

Property

The slope of a line is constant: no matter which two points you pick to compute the slope, you will always get the same value.

Because $m$ is constant for a given line, we can use the formula $m = \frac{\Delta y}{\Delta x}$ to find $\Delta y$ when we know $\Delta x$ , or to find $\Delta x$ when we know $\Delta y$ .

We can also tell whether a collection of data points lies on a straight line by computing slopes between them.

Overview

Lesson overview

Review the lesson summary and core properties without leaving the current page.

Overview

Section 1

The Core Formula: Slope and Y-Intercept

Property

The slope-intercept form for a linear equation is $y = mx + b$ , where $m$ is the slope of the line and the point $(0, b)$ is the y-intercept.

The slope formula between two points $(x_1, y_1)$ and $(x_2, y_2)$ is $m = \frac{y_2 - y_1}{x_2 - x_1}$ .

This formula calculates the ratio of the change in the y-coordinates (rise) to the change in the x-coordinates (run).

Section 2

Lines Have Constant Slope

Property

The slope of a line is constant: no matter which two points you pick to compute the slope, you will always get the same value.

Because $m$ is constant for a given line, we can use the formula $m = \frac{\Delta y}{\Delta x}$ to find $\Delta y$ when we know $\Delta x$ , or to find $\Delta x$ when we know $\Delta y$ .

We can also tell whether a collection of data points lies on a straight line by computing slopes between them.