Question

On coordinate plane, points (2, 1), (1, 5) and (0, 9) are connected through a line.

Drag a number to each box to represent the equation of the line.

Answer 1

To find the equation of the line that passes through the points (2, 1), (1, 5), and (0, 9), we can first determine the slope of the line, which can be done by using any two points. Let's use (2, 1) and (0, 9).

The formula for the slope \( m \) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points (2, 1) (let's call this \((x_1, y_1)\)) and (0, 9) (let's call this \((x_2, y_2)\)):
\[
m = \frac{9 - 1}{0 - 2} = \frac{8}{-2} = -4
\]

Now we can use the point-slope form of the equation of a line, which is:
\[
y - y_1 = m(x - x_1)
\]

Using point (2, 1):
\[
y - 1 = -4(x - 2)
\]

Now, we will simplify and rearrange this to slope-intercept form (y = mx + b):
\[
y - 1 = -4x + 8
\]
\[
y = -4x + 9
\]

So, the equation of the line is:
\[
y = -4x + 9
\]

If you are asked to fill in the specific boxes with coefficients for the equation \( y = mx + b \):
- The value for \( m \) (the slope) would be **-4**.
- The value for \( b \) (the y-intercept) would be **9**.

Fill the boxes with:
- Box for slope: **-4**
- Box for y-intercept: **9**