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. Image not found

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 of the line using two of the points.

1. Calculate the slope (m): The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

   Using the points \((1, 5)\) and \((2, 1)\): \[ m = \frac{1 - 5}{2 - 1} = \frac{-4}{1} = -4 \]

2. Using the point-slope form: The point-slope form of a line is: \[ y - y_1 = m(x - x_1) \] Let's use the point \((1, 5)\): \[ y - 5 = -4(x - 1) \] Simplifying this: \[ y - 5 = -4x + 4 \] \[ y = -4x + 9 \]

3. Equation of the line: The slope-intercept form of the equation we have derived is: \[ y = -4x + 9 \]

Thus, the equation of the line that passes through the points \((2, 1)\), \((1, 5)\), and \((0, 9)\) is \(y = -4x + 9\).

If you have boxes needing to be filled in related to the equation, you would place:

• The coefficient of \(x\) as \(-4\)
• The constant term as \(9\)

Answer 2

Y = [blank] x+[blank]

can you incorporate your answer into this?

Answer 3

Certainly! Based on the derived equation \(y = -4x + 9\), you can fill in the blanks as follows:

\[ Y = -4x + 9 \]

So, in the format you provided, it would be:

\[ Y = [-4] x + [9] \]

Therefore, the numbers to fill in the blanks are \(-4\) and \(9\).