7.7A Linear Equations

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 often denoted as 'm' in the equation y = mx + b.

Front

In the equation y = mx + b, what does 'b' represent?

Back

'b' represents the y-intercept, which is the point where the line crosses the y-axis.

Front

What is the formula to calculate 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 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.

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.

Front

How do you find the y-intercept from the equation y = -3x + 4?

Back

The y-intercept is the value of y when x = 0. For y = -3(0) + 4, the y-intercept is 4.

Front

What is the slope of the equation y = (-2/3)x + 8?

Back

The slope is -2/3.

Front

If Jane spends $8 for each lunch, how can we express her remaining money after x lunches?

Back

The remaining money can be expressed as y = 500 - 8x.

Front

What is the y-intercept of the equation y = -3x + 4?

Back

The y-intercept is 4.

Front

What does the term 'rise' refer to in the context of slope?

Back

'Rise' refers to the change in the y-coordinate (vertical change) between two points on a line.