Slope-Intercept Form Quiz

Study Notes

Slope-Intercept Form

The slope-intercept form of a linear equation is y = mx + b.
'y' represents the dependent variable.
'x' represents the independent variable.
'm' represents the slope of the line.
'b' represents the y-intercept of the line.

Understanding Slope (m)

Slope measures the steepness and direction of a line.
It represents the rate of change of 'y' with respect to 'x'.
A positive slope indicates an upward trend as 'x' increases.
A negative slope indicates a downward trend as 'x' increases.
A slope of zero indicates a horizontal line.
A slope that is undefined indicates a vertical line.
Slope can be calculated using two points (x₁, y₁) and (x₂, y₂) on the line: m = (y₂ - y₁) / (x₂ - x₁).

Interpreting the Y-intercept (b)

The y-intercept is the point where the line crosses the y-axis.
It represents the value of 'y' when 'x' is zero.
The y-intercept can be a positive, a negative number, or zero.

Practical Application in Graphing

Knowing the slope and y-intercept allows us to graph a line quickly.
First, plot the y-intercept on the y-axis.
Then, use the slope (rise over run) to find another point on the line, and connect the two points.

Examples

If the equation is y = 2x + 3, the slope is 2 and the y-intercept is 3.
If the equation is y = -x - 1, the slope is -1 and the y-intercept is -1.
If the equation is y = 5, the slope is 0 and the y-intercept is 5 (horizontal line).

Converting Other Forms to Slope-Intercept

Other forms of linear equations can be converted to slope-intercept form by isolating 'y'.
For example, the equation 2x + y = 5 can be rewritten as y = -2x + 5. This shows a slope of -2 and a y-intercept of 5.

Description

Test your understanding of the slope-intercept form of linear equations. This quiz covers key concepts like identifying the slope and y-intercept, along with practical applications. Perfect for students learning about linear functions.