Slope Intercept Equations

Front

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

Back

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

Front

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

Back

The y-intercept is the value of b in the equation y = mx + b, which is the point where the line crosses the y-axis.

Front

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

Back

The slope represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how much y changes for a unit change in x.

Front

How can you determine the slope from two points on a line?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What is the significance of a positive slope in a linear equation?

Back

A positive slope indicates that as the value of x increases, the value of y also increases, representing a direct relationship.

Front

What does a negative slope indicate about the relationship between x and y?

Back

A negative slope indicates that as the value of x increases, the value of y decreases, representing an inverse relationship.

Front

How do you convert a standard form equation to slope-intercept form?

Back

To convert from standard form Ax + By = C to slope-intercept form, solve for y to get y = (-A/B)x + (C/B).

Front

What is the y-intercept of the equation y = 3x + 5?

Back

The y-intercept is 5, which is the value of b in the slope-intercept form.

Front

If a line has a slope of 0, what does that mean?

Back

A slope of 0 means the line is horizontal, indicating that there is no change in y as x changes.

Front

What is the slope of the line represented by the equation y = -2x + 3?

Back

The slope of the line is -2.