11/2 Slope-Intercept Form 1

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you identify the y-intercept from a linear equation?

Back

The y-intercept is the value of y when x is 0, which can be found directly from the equation in slope-intercept form (y = mx + b) as the value of b.

Front

What does the slope of a line represent in a real-world context?

Back

The slope represents the rate of change of y with respect to x, indicating how much y changes for a unit change in x.

Front

How can you determine if a relationship is proportional from an equation?

Back

A relationship is proportional if it can be expressed in the form y = kx, where k is a constant and there is no constant term added or subtracted.

Front

What is the significance of the fixed fee in a linear equation representing a service charge?

Back

The fixed fee represents the y-intercept in the equation, indicating the initial cost before any additional charges based on hours worked.

Front

How do you write the equation of a line given the slope and y-intercept?

Back

Use the slope-intercept form: y = mx + b, substituting m for the slope and b for the y-intercept.

Front

What does it mean if the slope of a line is positive?

Back

A positive slope indicates that as x increases, y also increases, showing a direct relationship between the two variables.

Front

What is the formula to calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

In the equation y = mx + b, what does 'b' represent?

Back

In the equation, 'b' represents the y-intercept, which is the point where the line crosses the y-axis.

Front

How can you graph a linear equation in slope-intercept form?

Back

Start by plotting the y-intercept (0, b) on the graph, then use the slope (rise/run) to find another point on the line.