Writing Linear Equations (Rate of Change and Initial Value)

Front

What is a linear equation?

Back

A linear equation is an equation that models a straight line on a graph, typically in the form y = mx + b, where m is the slope (rate of change) and b is the y-intercept (initial value).

Front

What does the slope (rate of change) represent in a linear equation?

Back

The slope represents the rate at which the dependent variable (y) changes for every unit increase in the independent variable (x).

Front

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

Back

The y-intercept is the value of y when x is 0, representing the starting point or initial value of the dependent variable.

Front

How do you identify the slope from the equation y = 2x + 5?

Back

The slope is 2, indicating that for every 1 unit increase in x, y increases by 2 units.

Front

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

Back

The y-intercept is 4, meaning that when x is 0, y equals 4.

Front

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

Back

The equation is y = 3x + 2.

Front

If a linear equation is given as y = 5x + 10, what is the initial value?

Back

The initial value is 10.

Front

In the context of a word problem, what does 'constant rate' mean?

Back

'Constant rate' means that the change in the dependent variable occurs at a steady, unchanging pace over time.

Front

How can you determine if a linear equation is correct based on a graph?

Back

You can check if the line on the graph matches the slope and y-intercept indicated by the equation.

Front

What does it mean if a linear equation has a negative slope?

Back

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