Identifying equations

Front

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

Back

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

Front

What do the variables 'm' and 'b' represent in the equation y = mx + b?

Back

In the equation y = mx + b, 'm' represents the slope of the line, and 'b' represents the y-intercept, which is the point where the line crosses the y-axis.

Front

How do you interpret the slope 'm' in a real-world context?

Back

The slope 'm' represents the rate of change of y with respect to x. In a real-world context, it indicates how much y changes for a one-unit increase in x.

Front

What does the y-intercept 'b' indicate in a linear equation?

Back

The y-intercept 'b' indicates the value of y when x is 0. It represents the starting point of the line on the y-axis.

Front

How can you determine the equation of a line given a slope and a point on the line?

Back

You can use the point-slope form of the equation: y - y1 = m(x - x1), where (x1, y1) is the point on the line and m is the slope.

Front

What is the significance of the initial fee in a linear cost equation, such as a taxi fare?

Back

The initial fee in a linear cost equation represents a fixed cost that is incurred regardless of the variable cost per unit (e.g., per mile). It is the y-intercept in the equation.

Front

How do you graph a linear equation in slope-intercept form?

Back

To graph a linear equation in slope-intercept form (y = mx + b), start by plotting the y-intercept (b) on the y-axis, then use the slope (m) to determine the rise over run to plot additional points.

Front

What is the relationship between linear equations and real-world applications?

Back

Linear equations can model real-world situations where there is a constant rate of change, such as distance, cost, and time relationships.

Front

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

Back

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

Front

What is the formula for calculating the slope between two points (x1, y1) and (x2, y2)?

Back

The formula for calculating the slope (m) between two points is m = (y2 - y1) / (x2 - x1).