Question

Write an equation in standard form for the line that passes through the point 2 comma negative 1 and the point 6 comma 5.



Drag numbers to the blank lines and a symbol into the box to complete the equation.

Response area with 4 blank spaces
Blank space 1 empty
x
Blank space 2 empty
Blank space 3 empty
y equals
Blank space 4 empty
Answer options with 11 options.

Answer 1

To find the equation of the line in standard form (Ax + By = C) that passes through the points (2, -1) and (6, 5), we can follow these steps:

1. **Calculate the slope (m)**:
The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting our points (2, -1) and (6, 5):
\[
m = \frac{5 - (-1)}{6 - 2} = \frac{5 + 1}{4} = \frac{6}{4} = \frac{3}{2}
\]

2. **Use the point-slope form**:
The point-slope form of a line is given by:
\[
y - y_1 = m(x - x_1)
\]
Using the point (2, -1):
\[
y - (-1) = \frac{3}{2}(x - 2)
\]
Simplifying this:
\[
y + 1 = \frac{3}{2}(x - 2) \\
y + 1 = \frac{3}{2}x - 3 \\
y = \frac{3}{2}x - 4
\]

3. **Convert to standard form**:
To convert \(y = \frac{3}{2}x - 4\) to standard form \(Ax + By = C\), we rearrange the equation:
\[
-\frac{3}{2}x + y = -4
\]
Multiply through by -2 to eliminate the fraction:
\[
3x - 2y = 8
\]

Thus, in the standard form \(Ax + By = C\), we have the equation \(3x - 2y = 8\).

Filling in your response area with the suitable values, we have:

- Blank space 1: 3
- Blank space 2: -2
- Blank space 3: 8
- Blank space 4: 0 (as there is no addition in the standard form)

So, you can write the response as:
\[
3 \quad x \quad -2 \quad y = 8
\]