Linear Equations in the Real World

How can you graph a linear equation?

• Plot the y-intercept on the y-axis and use the slope to find another point, then draw a straight line through the points.

• Draw a curve that connects the x-intercept and y-intercept.

• Use a ruler to draw a vertical line at the y-intercept.

• Plot random points on the graph and connect them with a line.

What is the significance of the coefficients in a linear equation?

• Coefficients indicate the relationship between the variables; they show how much y changes for a unit change in x.

• Coefficients are used to determine the slope of the line only.

• Coefficients represent the y-intercept of the equation.

• Coefficients have no significance in a linear equation.

What is a linear equation?

• A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

• A linear equation is an equation that represents a curve when graphed.

• A linear equation is an equation that has no solutions.

• A linear equation is an equation that can only be written in the form y = b. It has no slope.

What does the slope (m) represent in a linear equation?

• The slope (m) represents the rate of change of the dependent variable (y) with respect to the independent variable (x).

• The slope (m) indicates the y-intercept of the line.

• The slope (m) represents the maximum value of the dependent variable (y).

• The slope (m) shows the distance between two points on the line.

What does the y-intercept (b) represent in a linear equation?

• The value of y when x is 0, representing the starting point of the line on the y-axis.

• The slope of the line, indicating how steep it is.

• The point where the line crosses the x-axis.

• The average value of y for all x values.

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

• Linear equations can model real-world situations where there is a constant rate of change, such as costs, earnings, and distances.

• Linear equations are only applicable in theoretical mathematics and have no real-world applications.

• Linear equations can only represent static situations without any change over time.

• Linear equations are used exclusively in physics and have no relevance to economics or social sciences.

How do you write the equation of a line given a slope and a y-intercept?

• y = mx + b, where m is the slope and b is the y-intercept

• y = b + mx, where b is the y-intercept and m is the slope

• y = mx^2 + b, where m is the slope and b is the y-intercept

• y = b - mx, where b is the y-intercept and m is the slope

What is the general form of a linear equation?

• Ax + By = C, where A, B, and C are constants.

• y = mx + b, where m is the slope and b is the y-intercept.

• x^2 + y^2 = r^2, which represents a circle.

• A + B = C, which is a simple addition equation.

How do you determine the x and y variables in a real-world scenario involving linear equations?

• The x variable represents the dependent variable, while the y variable represents the independent variable.

• The x variable typically represents the independent variable (like time or quantity), while the y variable represents the dependent variable (like total cost or earnings).

• The x variable is always a constant, while the y variable changes based on the x variable.

• The x variable represents the total cost, while the y variable represents the quantity sold.

What is the cost equation for renting a moped from Scoots Inc.?

• y = 0.25x + 15

• y = 0.50x + 20

• y = 0.75x + 10

• y = 0.60x + 25