Identifying Slope and Y-Intercept

Front

What is the y-intercept of a graph?

Back

The y-intercept is the point where the graph intersects the y-axis, represented as (0, b) in the equation y = mx + b.

Front

How do you find the y-intercept from an equation?

Back

To find the y-intercept from an equation in the form y = mx + b, set x = 0 and solve for y. The value of y is the y-intercept.

Front

What is the slope of a line?

Back

The slope of a line measures its steepness and direction, calculated as the change in y over the change in x (rise/run).

Front

How do you determine the slope from two points (x1, y1) and (x2, y2)?

Back

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

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as x increases, y also increases, meaning the line rises from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, meaning the line falls from left to right.

Front

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

Back

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

Front

If the equation of a line is y = 3x - 4, what is the y-intercept?

Back

The y-intercept is -4.

Front

If the equation of a line is y = -2x + 1, what is the slope?

Back

The slope is -2.

Front

What is the significance of the y-intercept in real-world applications?

Back

The y-intercept often represents the starting value or initial condition in real-world scenarios, such as revenue or population.