Linear Relationships Tutoring for Test

Front

What is a linear relationship?

Back

A linear relationship is a relationship between two variables that can be represented by a straight line on a graph. It can be described by a linear equation of the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope of a line 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 do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

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

Front

What is the y-intercept in a linear equation?

Back

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

Front

What is the equation of a line with a slope of 2 and a y-intercept of 3?

Back

The equation of the line is y = 2x + 3.

Front

If a taxi charges a flat fee plus a per-mile rate, how can you express the total cost?

Back

The total cost can be expressed as y = mx + b, where m is the per-mile rate, x is the number of miles, and b is the flat fee.

Front

What is the total cost for a taxi ride that charges $2.50 initial fee and $2.65 per mile for 10 miles?

Back

The total cost is y = 2.65(10) + 2.50 = $26.00.

Front

How do you interpret the slope of a graph in a real-world context?

Back

The slope indicates how much one quantity changes in relation to another. For example, if the slope is 5, it means for every unit increase in x, y increases by 5.

Front

What does it mean if the slope of a line is negative?

Back

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

Front

What is the profit per box if Emily sells greeting cards and the graph shows a profit of $7.50 per box?

Back

The profit per box is $7.50.