Question

The graph of a linear function has a slope of 5, and it passes through the point (–7, 5). What is the value of the dependent variable when the independent variable is equal to 2?

Answer 1

To find the value of the dependent variable, we use the point-slope form of the linear equation. Using the given slope of 5 and point (-7, 5), we first find the y-intercept to be 40. We then calculate the dependent variable's value to be 50 when the independent variable is 2.

Step-by-step explanation:

The student has asked about the value of the dependent variable when the independent variable is 2 for a given linear function that has a slope of 5, and passes through the point (–7, 5). To find this value, one should use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.

First, using the given point (–7, 5), we can find the y-intercept by substituting the slope and point into the equation:

y = 5x + b

5 = 5(-7) + b

b = 5 + 35

b = 40

So the equation of the line is y = 5x + 40. Now, to find the value of y when x is 2:

y = 5(2) + 40

y = 10 + 40

y = 50

Therefore, the value of the dependent variable when the independent variable is 2 is 50.

Answer 2

If we would have assigned a different value for x, the equation would have given us another value for y. We could instead have assigned a value for y and solved the equation to find the matching value of x.

In our equation y=x+7, we have two variables, x and y. The variable which we assign the value we call the independent variable, and the other variable is the dependent variable, since it value depends on the independent variable. In our example above, x is the independent variable and y is the dependent variable.

A function is an equation that has only one answer for y for every x. A function assigns exactly one output to each input of a specified type.

It is common to name a function either f(x) or g(x) instead of y. f(2) means that we should find the value of our function when x equals 2.