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.
y= x+

resposes:
-9
-5
-4
-2
-1
0
1
2
4
5
9

Answer 1

To find the equation of the line that passes through the given points, we can use the slope-intercept form of a linear equation, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

First, let's find the slope \( m \) using two of the points, say (2, 1) and (1, 5):

The slope formula is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using points (2, 1) and (1, 5):
\[
m = \frac{5 - 1}{1 - 2} = \frac{4}{-1} = -4
\]

Now that we have the slope \( m = -4 \), we can use one of the points to find the y-intercept \( b \). Let's use the point (2, 1):

Substituting into the equation:
\[
1 = -4(2) + b
\]
\[
1 = -8 + b
\]
\[
b = 1 + 8 = 9
\]

Now we have the slope \( m = -4 \) and the y-intercept \( b = 9 \). Therefore, the equation of the line is:
\[
y = -4x + 9
\]

To fill in the blanks:
\[
y = -4x + 9
\]

So, the correct responses for the boxes would be:
- \( -4 \) for the coefficient of \( x \)
- \( 9 \) for the constant term

Therefore, the complete equation is:
\[
y = -4x + 9
\]