Question

A line is shown on the coordinate plane.

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 start by determining the slope (m) and then use the point-slope form of the equation.

1. **Calculate the slope (m)**:
The slope formula is given by:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
We can use the points (2, 1) and (1, 5) to find the slope:

\[
m = \frac{5 - 1}{1 - 2} = \frac{4}{-1} = -4
\]

2. **Use the point-slope form**:
The point-slope form of the equation of a line is:
\[
y - y_1 = m(x - x_1)
\]
Using point (2, 1):
\[
y - 1 = -4(x - 2)
\]

Expanding this:
\[
y - 1 = -4x + 8
\]
\[
y = -4x + 9
\]

This gives us the equation of the line in slope-intercept form \(y = mx + b\):

\[
y = -4x + 9
\]

From this equation, we can identify that the slope \(m\) is \(-4\), and the y-intercept \(b\) is \(9\).

### Summary:
So, to represent the equation of the line, you can fill in the boxes with:
- Slope (m): **-4**
- Y-intercept (b): **9**

Hence:
\[
y = -4x + 9
\]