Write an equation from slope-intercept form (y=mx+b ) from the table below.

Question

x -y
0 -7
6-2
12- -3
18- -8
y =

Answer 1

To write an equation in slope-intercept form (y = mx + b) using the table provided, we need to calculate the slope (m) and the y-intercept (b). The slope is the change in y divided by the change in x between two points.

Looking at the table:

\[
\begin{array}{c|c}
x & y \\
\hline
0 & -7 \\
6 & -2 \\
12 & 3 \\
18 & 8 \\
\end{array}
\]

We can pick any two points to calculate the slope. Let's use the first two points:

Point 1: (0, -7)
Point 2: (6, -2)

The slope (m) is given by:
\[
m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - (-7)}{6 - 0} = \frac{5}{6}
\]

The slope of the line is 5/6.

Now, let's find the y-intercept (b). Since the first point's x-value is 0, the corresponding y-value is the y-intercept. This is because when x = 0, y = b in the slope-intercept equation.

So, the y-intercept (b) is -7.

Therefore, the equation in slope-intercept form with the calculated slope and y-intercept is:

y = (5/6)x - 7

Answer 2

Write an equation from slope-intercept form (y=mx+b ) from the table below. Click Here for Help Video.

x-y
6 - 10
12 - 14
18 -18
y =

18
18
18
18

Answer 3

To write an equation in slope-intercept form (y = mx + b) from the given data, we first calculate the slope (m) by finding the change in y divided by the change in x between any two distinct points.

Given the table:

```
x | y
---------
6 | -10
12 | -14
18 | -18
```

Let's calculate the slope using the first two points:

Point 1: (6, -10)
Point 2: (12, -14)

The slope (m) is:
m = (y2 - y1) / (x2 - x1)
m = (-14 - (-10)) / (12 - 6)
m = (-14 + 10) / (6)
m = -4 / 6
m = -2 / 3

So, the slope is -2/3.

Next, to find the y-intercept (b), we can use the fact that the line must pass through any of the given points. Let's use Point 1 (6, -10) for this:

Since y = mx + b, we substitute x and y with the coordinates of Point 1, and m with our calculated slope:

-10 = (-2/3)(6) + b

Now, solve for b:

-10 = -4 + b
b = -10 + 4
b = -6

The y-intercept (b) is -6.

Therefore, the equation in slope-intercept form is:

y = (-2/3)x - 6