Linear Equations and Intercepts

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (positive or negative).

Front

How do you find the y-intercept of a linear equation?

Back

To find the y-intercept, set x = 0 in the equation and solve for y. The y-intercept is the point where the line crosses the y-axis.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What does it mean if a slope is undefined?

Back

An undefined slope occurs in a vertical line, where the change in x is zero, leading to division by zero in the slope formula.

Front

How do you determine if a line is increasing or decreasing?

Back

A line is increasing if the slope is positive (rises from left to right) and decreasing if the slope is negative (falls from left to right).

Front

What is the formula for calculating 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

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept indicates the value of y when x is zero. It is the point where the line crosses the y-axis.

Front

How can you identify the range of a linear function from its graph?

Back

The range can be identified by looking at the y-values covered by the graph. It includes all y-values that the line reaches.