A line is shown on the coordinate plane.

Question

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

Y = x+

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

-9 -5 -4 -2 -1 0 1 2 4 5 9

Answer 1

To find the equation of the line that passes through the points (2, 1), (1, 5), and (0, 9), we first need to determine the slope (m) of the line.

Let's calculate the slope using two of the points, say (1, 5) and (2, 1):

\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 5}{2 - 1} = \frac{-4}{1} = -4 \]

Now that we have the slope \( m = -4 \), we can use one of the points to find the y-intercept (b). We can use the point (1, 5) for this:

Using the slope-intercept form of the line \( y = mx + b \):

\[ 5 = -4(1) + b \] \[ 5 = -4 + b \] \[ b = 5 + 4 = 9 \]

Now we can write the equation of the line:

\[ y = -4x + 9 \]

In the given equation format \( y = x + \), we need to express it in that form:

Since we have \( y = -4x + 9 \), this can be written as:

\[ y = -4x + 9 \]

Thus, we can fill in the boxes:

Y = -4x + 9

So the complete expression is:

-9 in the second box.

So the final answer is:

Y = -4x + 9.