Question

Graph the line that passes through the points left parenthesis, 8, comma, minus, 7, right parenthesis(8,−7) and left parenthesis, minus, 7, comma, 8, right parenthesis(−7,8) and determine the equation of the line.

Answer 1

To find the equation of the line that passes through the points \( (8, -7) \) and \( (-7, 8) \), we can follow these steps:

1. **Calculate the slope (m)** of the line using the slope formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Here, \( (x_1, y_1) = (8, -7) \) and \( (x_2, y_2) = (-7, 8) \).

Substitute the values into the formula:
\[
m = \frac{8 - (-7)}{-7 - 8} = \frac{8 + 7}{-15} = \frac{15}{-15} = -1
\]

2. **Use the point-slope form of the line** to find the equation of the line. The point-slope form is given by:
\[
y - y_1 = m(x - x_1)
\]
We can use one of the points, say \( (8, -7) \):
\[
y - (-7) = -1(x - 8)
\]
Simplifying the equation:
\[
y + 7 = -1(x - 8)
\]
\[
y + 7 = -x + 8
\]
\[
y = -x + 1
\]

3. **Convert to slope-intercept form**:
The equation of the line in slope-intercept form is:
\[
y = -x + 1
\]

4. **Graph the line**:
To graph \( y = -x + 1 \):
- Start with the y-intercept (0, 1).
- The slope is -1, meaning for every 1 unit to the right, the line goes down 1 unit.

Now, you can plot the points \( (8, -7) \) and \( (-7, 8) \), and draw a straight line through them, following the slope.

Thus, the equation of the line is:
\[
\boxed{y = -x + 1}
\]