Which Table Represents a Linear Function
Which Table Represents a Linear Function
Part I.
How Linear Equations relate to Tables Of Values
Equations as Relationships
The equation of a line expresses a relationship betwixt x and y values on the coordinate airplane. For instance, the equation
$$y = x$$
expresses a human relationship where every x value has the exact same y value. The equation
$$ y = 2x $$
expresses a relationship in which every y value is double the x value, and
$$ y = x + 1 $$
expresses a relationship in which every y value is 1 greater than the 10 value.
So what about a Table Of Values?
Since, every bit we simply wrote, every linear equation is a relationship of ten and y values, nosotros tin create a tabular array of values for any line. These are simply the
$$ x $$
and
$$ y $$
values that are
true
for the given line. In other words, a table of values is just some of the points that are on the line.
Example i
Equation:
$$ \red y = \blue x + i $$
Table of Values
| $$ \blue x \text { value} $$ | Equation | $$ \red y \text{ value} $$ |
| y = 10 + 1 | ||
| $$ \blueish three $$ | $$y = ( \blue iii ) + one$$ | $$ \red 4 $$ |
| $$ \blue four $$ | y = ($$ \blue iv $$ ) + ane | $$ \red 5 $$ |
| $$ \blue five $$ | $$ y = (\blue v ) + 1$$ | $$ \red six $$ |
| $$ \blueish six $$ | $$ y = ( \blue 6) + one $$ | $$ \red seven $$ |
Example two
Equation:
y = 3x + 2
Table of Values
| Ten Value | Equation | Y value |
| y = 3x + 2 | ||
| one | y = 3(1) + 2 | 5 |
| 2 | y = 3(2) + 2 | 7 |
| 3 | y = 3(iii) + two | 11 |
| 4 | y = 3(four) + 2 | fourteen |
So, to create a table of values for a line, simply pick a set of ten values, substitute them into the equation and evaluate to get the y values.
Exercise
Creating a Table of Values
Problem i
Create a table of values of the equation
y = 5x + two.
Create the table and choose a set of x values.
| 10 Value | Equation | Y value |
| y = 5x + ii | ||
| one | ||
| 2 | ||
| 3 | ||
| four |
Substitute each x value (left side column) into the equation.
| Ten Value | Equation | Y value |
| y = 5x + 2 | ||
| 1 | y = five(1) + 2 | |
| ii | y = 5(2) + 2 | |
| three | y = 5(three) + two | |
| 4 | y = 5(4) + ii |
Evaluate the equation (center cavalcade) to get in at the y value.
| X Value | Equation | Y value |
| y = 5x + ii | ||
| 1 | y = 5(1) + ii | 7 |
| ii | y = 5(ii) + 2 | 12 |
| 3 | y = 5(3) + two | 17 |
| iv | y = 5(4) + two | 22 |
An Optional step, if you lot want, you tin can omit the middle column from your table, since the table of values is really just the x and y pairs.
(Nosotros used the heart column simply to help us get the y values)
| Ten Value | Y Value |
| ane | 7 |
| 2 | 12 |
| 3 | 17 |
| 4 | 22 |
Problem 2
Create a table of values of the equation
y = −6x + 2.
Create the table and choose a set of x values.
| X Value | Equation | Y value |
| y = −6x + two | ||
| 1 | ||
| 2 | ||
| iii | ||
| four |
Substitute each x value (left side column) into the equation.
| X Value | Equation | Y value |
| y = −6x + 2 | ||
| 1 | y = −6(1) + 2 | |
| 2 | y = −6(2) + 2 | |
| three | y = −six(3) + two | |
| 4 | y = −6(iv) + 2 |
Evaluate the equation (middle column) to arrive at the y value.
| X Value | Equation | Y value |
| y = −6x + 2 | ||
| 1 | y = −6(1) + 2 | -four |
| 2 | y = −6(ii) + ii | -10 |
| 3 | y = −6(three) + two | -16 |
| four | y = −6(four) + 2 | -22 |
An Optional step, if you want, you tin can omit the middle column from your table, since the table of values is really just the 10 and y pairs .(We used the middle column merely to assist us go the y values)
| X Value | Y value |
| one | -four |
| 2 | -10 |
| 3 | -16 |
| 4 | -22 |
Problem 3
Create a table of values of the equation
y = −6x − 4
Create the table and cull a fix of x values
| X Value | Equation | Y value |
| y = −6x − 4 | ||
| one | ||
| ii | ||
| 3 | ||
| 4 |
Substitute each x value (left side column) into the equation.
| X Value | Equation | Y value |
| 1 | y = −six(ane) − four | |
| 2 | y = −6(2) − four | |
| three | y = −six(three) − 4 | |
| 4 | y = −6(four) − iv |
Evaluate the equation (heart column) to get in at the y value.
| X Value | Equation | Y value |
| 1 | y = −vi(1) − 4 | -10 |
| 2 | y = −6(2) − four | -xvi |
| 3 | y = −6(3) − 4 | -22 |
| iv | y = −half-dozen(4) − 4 | -28 |
An Optional step, if yous want, you can omit the middle column from your tabular array, since the table of values is really but the x and y pairs.
(We used the centre column only to help the states get the y values)
| X Value | Y value |
| ane | -10 |
| 2 | -xvi |
| three | -22 |
| four | -28 |
Function Ii.
Writing Equation from Table of Values
Often, students are asked to write the equation of a line from a table of values. To solve this kind of problem, simply chose any 2 points on the tabular array and follow the normal steps for writing the equation of a line from two points.
Problem four
Cull whatsoever two x, y pairs from the table and calculate the slope. Since, I like to work with easy, small-scale numbers I chose (0, 3) and (one, 7).
| X Value | Y value |
| 3 | |
| 1 | 7 |
| 2 | 11 |
| 3 | 15 |
Observe the value of ‘b’ in the slope intercept equation.
y = mx + b
y = 4x + b
Since our table gave usa the point (0, 3) we know that ‘b’ is 3. Recall ‘b’ is the y-intercept which, luckily, was supplied to us in the table.
Answer:
y = 4x + three
If you’d like, you could check your reply past substituting the values from the table into your equation. Each and every x, y pair from the tabular array should piece of work with your answer.
Problem 5
Write the equation from the table of values provided below.
| Ten Value | Y value |
| two | 8 |
| 4 | ix |
| 6 | 10 |
Find the value of ‘b’ in the gradient intercept equation.
Now that nosotros know the value of b, we can substitute it into our equation.
Answer:
y = ½ten + 7
If you’d like, you could check your reply by substituting the values from the table into your equation. Each and every x, y pair from the table should work with your answer.
Trouble half-dozen
Find the value of ‘b’ in the slope intercept equation.
Now that we know the value of b, we can substitute information technology into our equation.
Answer:
y =
x + 4
If you’d similar, you could check your answer by substituting the values from the tabular array into your equation. Each and every 10, y pair from the tabular array should piece of work with your answer.
Challenge Problem
Why tin can yous
not
write the equation of a line from the table of values below?
The reason that this table could
not
correspond the equation of a line is because the slope is inconsistent. For instance the gradient of the ii points at the top of the table (0, one) and (1, 3) is dissimilar from the slope at the lesser (2, eight) and (3, 11).
Which Table Represents a Linear Function
Source: https://www.mathwarehouse.com/algebra/linear_equation/linear-equation-table-examples-graphs.php
