Question

4ae

Directions: Work out each problem completely including explaining why you solved the
problem the way you did.
1. Lydia was given an x-y table like the one below (6 points)
Unit Review
x
5
4
10
7
y
19
15
39
27
She decided that the equation that matches this x-y table is y = 3x + 4. Prove to Lydia
that this equation does NOT work for every coordinate, and then show her the correct
equation/function that matches the x-y table above.

Answer 1

• Lydia's equation does not work for x=4: 3(4)+4 ≠ 15
• correct equation: y = 4x -1

Explanation:

You want an equation that matches the given x-y table:

x = 5, 4, 10, 7

y = 19, 15, 39, 27

Lydia's solution

Lydia's equation works for the first point in this table, (x, y) = (5, 19):

3(5) +4 = 19

However, it does not work for any other points in the table. For example, (x, y) = (4, 15):

3(4) +4 ≠ 15.

This is also shown in the attached graph, where we have graphed the table values along with Lydia's equation.

Equation

We like to graph points in a table as a way to see what kind of relation we're dealing with. Here, the points lie on a straight line, so a linear equation is needed. It will be different from Lydia's, which does not match the data.

The slope of the line can be found using the slope equation:

m = (y2 -y1)/(x2 -x)

Using points (x, y) = (4, 15) and (5, 19) we have ...

m = (19 -15)/(5 -4) = 4

The y-intercept of the line can be found using the slope-intercept equation, solved for "b".

b = y -mx

b = 15 -4(4) = -1 . . . . . . . using (x, y) = (4, 15) and m=4

The slope-intercept equation for the line is ...

y = mx +b

y = 4x -1

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Additional comment

We can see on the graph that each point is 1 unit below 4 times the x-value. This confirms our equation is correct.

This graphing calculator can also write a linear regression equation for the data points. That will give the same result.

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