Work with Functions

Question

What is the rule for this function table X:0,1,2,3,4  Y:7,8,9,10,11   And after you find the rule tell me whats the Value of y when x = 8. Then i need to know what would be the value of x when y = 35.                                       .

Answer 1

One way to tackle this problem is to graph the points to determine the relationship between y and x. If we write the coordinate pairs we have (0, 7), (1, 8), (2, 9), (3, 10), (4, 11). When you plot those you will notice a linear relationship.

To get the equation of the line, which will be the function rule, find the y-intercept and the slope. Remember that the y-intercept is where the line crosses the y-axis, so x = 0. One of our points is (0, 7). x = 0 and y = 7. We will use 7 for the y-intercept in the equation.

To find the slope we need the coordinates of any two points on the line. Lets use (0, 7) for point 1 and

(3, 10) for point 2. We could use any two points and, hopefully, get the same calculated slope. The formula for slope is (y2-y1)/(x2-x1). 

Point 1 is (0, 7) so x1 = 0 and y1 = 7. Point 2 is (3, 10) so x2 = 3 and y2 = 10. Now substitute into the slope formula -->   (10 - 7) / (3 - 0) = 3/3 = 1. So slope = 1

Now write the equation of the line in y = mx + b form. m is the slope and b is the y-intercept.

So y = 1x + 7. Now the 1 can be "invisible" so we normally write this y = x + 7. This is the rule, the equation of the line.

To find the values for y when x = 8, just substitute for x in the equation above:

      y = 8 + 7 = 15    when x = 8, y = 15

When y = 35, substitute 35 for y and then solve for x

      35 = x + 7

Subtract 7 from both sides -->  28 = x    when y = 35, x = 28

      

Answer 2

If I understand the question correctly - you're looking for a formula to express a graph going through the listed points.

Okay... if you plot this on a graph it looks to have a slope of 1/1 (that is, for every one it moves over via 'x' , it moves up one. When x = 0, y = 7, so we know we have to add 7 to the equation.

I'm seeing y = x + 7.
When x = 8, y would be equal to 15.
If you flip the equation (x = y -7), you'll find when y = 35, x will equal 28.