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 determine the equation of the line that passes through the points (2, 1), (1, 5), and (0, 9), we need to first find the slope of the line and then use the point-slope form of a line.

1. **Calculate the slope (m):**
We can use the slope formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
For the points (1, 5) and (2, 1):
\[
m = \frac{1 - 5}{2 - 1} = \frac{-4}{1} = -4
\]

2. **Find the intercept (b):**
We can use one of the points to find the y-intercept (b). Let's use the point (2, 1):
\[
y = mx + b \implies 1 = -4(2) + b
\]
\[
1 = -8 + b \implies b = 9
\]

3. **Create the equation of the line:**
The equation of the line in slope-intercept form (y = mx + b) is:
\[
y = -4x + 9
\]

So, the equation for the line that connects the three points is **y = -4x + 9**. If you need the specific numbers to drag to different boxes, you’d place -4 in the box for the slope and 9 in the box for the y-intercept.