Question

Find the equation of the linear function represented by the table below in slope-intercept form.
xx 00 11 22 33 44
yy minus, 9−9 minus, 4−4 11 66 1111
Answer
Attempt 1 out of 2

y, equalsy=

Answer 1

To find the equation of the linear function from the given data in the table, we first identify the coordinates from the pairs (x, y):

- \( (0, -9) \)
- \( (1, -4) \)
- \( (2, 1) \)
- \( (3, 6) \)
- \( (4, 11) \)

Now, we can calculate the slope \( m \) using the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points \( (0, -9) \) and \( (1, -4) \):

\[
m = \frac{-4 - (-9)}{1 - 0} = \frac{-4 + 9}{1} = \frac{5}{1} = 5
\]

Now that we have the slope, we can 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. From the first point \( (0, -9) \), we know that when \( x = 0 \), \( y = -9 \). Thus, the y-intercept \( b = -9 \).

Now we can write the equation:

\[
y = 5x - 9
\]

So the final answer is:

\[
y = 5x - 9
\]