Question

Find the equation of the linear function represented by the table below in slope-

intercept form.
10
12

Answer 1

The equation of the linear function represented by the table in slope-intercept form is y = 1x + 2.

Step-by-step explanation:

To find the equation of the linear function in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, we can use the given table. The table provides two points (x, y): (10, ?) and (12, ?).

The slope (m) can be calculated using the formula:

`\[m = \frac{\text{change in } y}{\text{change in } x}.\]`

Using the points (10, ?) and (12, ?), the change in y is 2 (12 - 10) and the change in x is 1 (since x increases by 1 unit from 10 to 12). Therefore, the slope (m) is 2/1, which simplifies to 2.

Now that we have the slope (m), we can use one of the points to find the y-intercept (b). Let's use the point (10, ?):

`\[y = mx + b\]`

`\[?\ = 2(10) + b\]`

`\[?\ = 20 + b\]`

Solving for b, we find that b is 2. Now we can substitute the values of m and b back into the slope-intercept form:

`\[y = 2x + 2.\]`

So, the final equation of the linear function is
`\(y = 2x + 2\)`, representing the relationship between x and y based on the given table.

Answer 2

The picture attached has the table that repfesents the linear function to find the equation.

Answer:

• y = 10x - 6

Step-by-step explanation:

A linear function is characterized by a constant slope and a unique y-intercept.

Let m be the slope and b the y-intercept of a linear function. Then, slope-intercept equation has the form:

• y = mx + b.

Using any two pair of points (x,y) from the table you can determine the values of m and b.

The table is:

x 0 1 2 3 4

y -6 4 14 24 34

You know that it is a linear function because for constant increases of the x-values (1 unit in the table) there is a constant increase of the y-values (10 in the table).

The slope, m, is calculated as:

• m = [change in y] / [change in x] = Δy / Δx = [14 - 4] [2 - 1] = 10

As said, you could have used any two points to calculate m,

The y-intercept, b, is the value of the function, y, when x = 0.

• From the table you can observe that when x = 0, the value of y is - 6; so b = - 6.

Thus, the equation of the linear function represented in the table in slope-intercept form is:

• y = 10x - 6.