Question

x-y
-5- -4
-10- -8
-15- -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 of values, we first need to determine the slope (m) and the y-intercept (b).

Let's analyze the data given in the table, interpreting it as pairs of (x, y) coordinates:

- From the first row: (5, -4)
- From the second row: (10, -8)
- From the third row: (15, -12)

Now, let’s find the slope (m) using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

We'll use the first two points for this calculation:

\[
m = \frac{-8 - (-4)}{10 - 5} = \frac{-8 + 4}{10 - 5} = \frac{-4}{5} = -\frac{4}{5}
\]

Next, we can use the slope and one of the points to find the y-intercept (b). Choosing the point (5, -4):

Using the slope-intercept form:
\[
y = mx + b
\]
Substituting the values of m and the point (5, -4):
\[
-4 = -\frac{4}{5}(5) + b
\]
Calculating:
\[
-4 = -4 + b
\]
So:
\[
b = 0
\]

Now we have the slope and the y-intercept:
- Slope (m) = -\frac{4}{5}
- Y-intercept (b) = 0

Thus, the equation in slope-intercept form is:
\[
y = -\frac{4}{5}x
\]