Find the slope and y-intercept

Front

What is the slope of a linear equation?

Back

The slope of a linear equation represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It is calculated as the change in y divided by the change in x (rise/run).

Front

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

Back

The y-intercept of a linear equation is the value of y when x is equal to zero. It can be found by substituting x = 0 into the equation and solving for y.

Front

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

Back

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

Front

What does a positive slope indicate about a linear relationship?

Back

A positive slope indicates that as the independent variable (x) increases, the dependent variable (y) also increases, showing a direct relationship.

Front

What does a negative slope indicate about a linear relationship?

Back

A negative slope indicates that as the independent variable (x) increases, the dependent variable (y) decreases, showing an inverse relationship.

Front

What is the significance of the y-intercept in a graph?

Back

The y-intercept is the point where the line crosses the y-axis, indicating the value of the dependent variable when the independent variable is zero.

Front

How can you convert the standard form of a linear equation to slope-intercept form?

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y by isolating it on one side of the equation.

Front

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

Back

The slope of the line represented by the equation y = -3x is -3.

Front

What is the y-intercept of the equation 2y = -4x + 10?

Back

To find the y-intercept, set x = 0. The equation becomes 2y = 10, so y = 5. Thus, the y-intercept is 5.

Front

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

Back

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