Use Patterns to Write and Solve Equations

Front

What is an equation?

Back

An equation is a mathematical statement that asserts the equality of two expressions, typically containing variables.

Front

What does the variable 't' represent in the equation t=4d+5?

Back

In the equation t=4d+5, 't' represents the total or output value based on the input value 'd'.

Front

How do you find the value of 'y' using the equation y=4x-4 when x=3?

Back

Substituting x=3 into the equation gives y=4(3)-4, which simplifies to y=12-4, so y=8.

Front

What is the slope in the equation y=2x+7?

Back

The slope in the equation y=2x+7 is 2, indicating that for every increase of 1 in x, y increases by 2.

Front

What does it mean for 'y' to be 2 more than 'x'?

Back

It means that the value of 'y' is obtained by adding 2 to the value of 'x'.

Front

How can you represent a relationship between two variables in a table?

Back

You can represent a relationship by listing pairs of values for the variables, showing how one variable changes in relation to the other.

Front

What is the purpose of using patterns in equations?

Back

Using patterns helps to identify relationships between variables, allowing for predictions and solving for unknowns.

Front

If each Winkydiddle costs $3.50, how much do 4 Winkydiddles cost?

Back

4 Winkydiddles cost 4 x $3.50 = $14.00.

Front

What is the y-intercept in the equation y=4x-4?

Back

The y-intercept is -4, which is the value of y when x=0.

Front

How do you write an equation from a given table of values?

Back

To write an equation from a table, identify the pattern in the values and express it in the form of y=mx+b, where m is the slope and b is the y-intercept.