Determining Slope and Y-intercept from Slope-Intercept Form

Front

What does the slope (m) represent in the slope-intercept form of a linear equation?

Back

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

Front

What is the y-intercept (b) in the slope-intercept form of a linear equation?

Back

The y-intercept (b) is the value of y when x is 0. It represents the point where the line crosses the y-axis.

Front

How do you identify the slope and y-intercept from the equation y = mx + b?

Back

In the equation y = mx + b, 'm' is the slope and 'b' is the y-intercept.

Front

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

Back

The slope of the line is -2.

Front

What is the y-intercept of the line represented by the equation y = 4x - 1?

Back

The y-intercept of the line is -1.

Front

How can you convert the standard form of a linear equation, Ax + By = C, to slope-intercept form?

Back

To convert to slope-intercept form, solve for y: y = (-A/B)x + (C/B). The slope is -A/B and the y-intercept is C/B.

Front

What does a slope of 0 indicate about a line?

Back

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

Front

What does a negative slope indicate about the direction of a line?

Back

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

Front

What is the graphical representation of the equation y = 1/3x - 2?

Back

The graph is a straight line that crosses the y-axis at -2 and has a slope of 1/3, rising slowly as it moves to the right.

Front

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

Back

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