Linear Equations

Linear Relationships

Identify whether each pair of variables is proportional or non-proportional: 1) The number of apples bought and total cost if each apple costs the same. 2) The amount of paint needed for a wall and the wall's dimensions when the paint covers a specific area per unit.

Linear Relationships

Identify whether each pair of variables is proportional or non-proportional: 1) The hours worked and total pay at an hourly wage. 2) The temperature in Celsius and Fahrenheit.

Slope

Find the slope of the line that passes through the points (1, 2) and (4, 8).

Slope

Find the slope of the line that passes through the points (-3, -1) and (2, 4).

Rate of Change

If the temperature changes from 20°C to 30°C over 5 hours, what is the rate of change in temperature per hour?

Rate of Change

A bus travels 30 miles in the first hour and 60 miles in the second hour. What is the rate of change of distance traveled per hour?

Constant of Proportionality

If y is directly proportional to x and y = 18 when x = 3, what is the constant of proportionality k?

Constant of Proportionality

If y = 10 when x = 2, what is the constant of proportionality in the equation y = kx?

Slope-Intercept Form

Write the equation of a line in slope-intercept form with a slope of -3 and passing through the point (0, 5).

Slope-Intercept Form

Write the equation of a line with a slope of 2 and a y-intercept of 7.

Y-intercept

Find the y-intercept of the line described by the equation 4x + 3y = 12.

Y-intercept

Determine the y-intercept for the equation 5x - 6y = 30.

Graphing Solutions of Linear Functions

Graph the equation y = 3x - 2 and list at least three ordered pairs that are solutions.

Graphing Solutions of Linear Functions

Graph the equation y = -x + 5. Identify the x-intercept and at least two solutions.

Standard Form

Convert the equation y = 3x + 2 to standard form Ax + By = C.

Standard Form

Rewrite the equation y = -2x + 4 in standard form.

Systems of Equations

Solve the following system of equations: 1) 3x + 4y = 12; 2) 2x - y = 3.

Systems of Equations

Solve the system of equations: 1) x + 2y = 10; 2) 2x - 3y = -1.

Constant of Proportionality

The constant factor that relates two variables that are proportional to each other, expressed in the form y = kx, where k is the constant of proportionality.

Rate of Change

The ratio that describes how much one quantity changes in relation to another quantity, often represented as the slope in a linear function.

Constant

A fixed value that does not change regardless of the conditions or circumstances; in algebra, it is often a number without a variable.

Solution to a Linear Equation

A value or set of values that, when substituted into the equation, make it true; it typically represents a point at which the graph of the equation intersects the coordinate axes.

System of Linear Equations

A set of two or more linear equations with the same variables, which can be solved simultaneously to find the values of the variables that satisfy all equations in the system.