Question

A line passes through the point 7 comma negative 4 and the point negative 3 comma 4.



Drag numbers to the blanks to complete the equation of the line.

Response area with 2 blank spaces
4 x plus
Blank space 1 empty
y equals
Blank space 2 empty
Answer options with 8 options.

Answer 1

To find the equation of the line passing through the points \( (7, -4) \) and \( (-3, 4) \), we can follow these steps:

1. **Calculate the slope (m)** of the line using the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Here, \( (x_1, y_1) = (7, -4) \) and \( (x_2, y_2) = (-3, 4) \).

\[
m = \frac{4 - (-4)}{-3 - 7} = \frac{4 + 4}{-10} = \frac{8}{-10} = -\frac{4}{5}
\]

2. **Use the point-slope form** of the line equation:

\[
y - y_1 = m(x - x_1)
\]

We can use the point \( (7, -4) \):

\[
y - (-4) = -\frac{4}{5}(x - 7)
\]

Simplifying this:

\[
y + 4 = -\frac{4}{5}x + \frac{28}{5}
\]

Subtracting 4 from both sides:

\[
y = -\frac{4}{5}x + \frac{28}{5} - \frac{20}{5}
\]
\[
y = -\frac{4}{5}x + \frac{8}{5}
\]

3. **Rearrange to the standard form** \( Ax + By = C \):

Multiply through by 5 to eliminate the fractions:

\[
5y = -4x + 8
\]

Rearranging gives:

\[
4x + 5y = 8
\]

Now, we have the equation of the line:

\[
4x + 5y = 8
\]

So, filling in the blanks in the original prompt:

**Blank space 1:** 5
**Blank space 2:** 8

Thus the final answer would be:

4x + **5**y = **8**