6th 4-10 Relate Tables Graphs and Equations

Front

What is the relationship between the height of a skeleton (h) and the length of the femur bone (f)?

Back

The height of a skeleton is about 30 inches taller than twice the length of the femur bone. This can be represented by the equation: h = 2(f) + 30.

Front

What does the equation t = d + 4 represent in the context of donations?

Back

In this equation, t represents the total amount of donations, d represents the other donations collected, and 4 is the additional amount added by Kate's father.

Front

If the width of a rectangle is 12, and the length is 1/3 of the width, what is the length?

Back

The length is 4, calculated as follows: Length = 1/3 * Width = 1/3 * 12 = 4.

Front

What is the equation that represents the total donations when Kate's father adds $4 to the other donations?

Back

The equation is t = d + 4, where t is the total and d is the other donations.

Front

How do you represent a linear relationship in a table with an equation?

Back

You can represent a linear relationship with an equation in 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 in a graph?

Back

The slope represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Front

What is the y-intercept in the equation y = mx + b?

Back

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

Front

How can you determine the equation of a line from a table of values?

Back

You can determine the equation by finding the slope (m) using two points from the table and then using one of the points to solve for the y-intercept (b).

Front

What is the formula to calculate the slope (m) between two points (x1, y1) and (x2, y2)?

Back

The formula for slope is m = (y2 - y1) / (x2 - x1).

Front

If a table shows that for every increase of 1 in x, y increases by 2, what is the slope?

Back

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