Question

x-y
-7- 0
0- 4
7-8
14-12
Write an equation from slope-intercept form (y=mx+b ) from the table below.

Answer 1

To write an equation in slope-intercept form (y = mx + b) from the given table, we first need to determine the slope (m) and the y-intercept (b) of the line represented by the points in the table.

From the table, the given points are:

1. (-7, 0)
2. (0, 4)
3. (7, 8)
4. (14, 12)

**Step 1: Calculate the slope (m)**

We can choose any two points to find the slope. Let's take the first two points: (-7, 0) and (0, 4).

The formula for the slope (m) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

Substituting the points (-7, 0) and (0, 4):

\[
m = \frac{4 - 0}{0 - (-7)} = \frac{4}{7}
\]

**Step 2: Determine the y-intercept (b)**

The y-intercept is the value of y when x = 0. From the second point (0, 4), we see that when \(x = 0\), \(y = 4\). So, \(b = 4\).

**Step 3: Write the equation**

Now we can substitute the values of m and b into the slope-intercept form:

\[
y = \frac{4}{7}x + 4
\]

This is the equation in slope-intercept form that corresponds to the given table of values.