Question

Graph with a point at negative 6, -6 and another point at 2, 5 write an equation

Answer 1

To find the equation of the line passing through the points \((-6, -6)\) and \((2, 5)\), we can use the slope-intercept form of a line, which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

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

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

Using the points \((-6, -6) = (x_1, y_1)\) and \((2, 5) = (x_2, y_2)\):

\[
m = \frac{5 - (-6)}{2 - (-6)} = \frac{5 + 6}{2 + 6} = \frac{11}{8}
\]

So, the slope \(m\) is \(\frac{11}{8}\).

2. **Use the point-slope form of the equation** of a line, which is:

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

Using one of the points, say \((-6, -6)\):

\[
y - (-6) = \frac{11}{8}(x - (-6))
\]
\[
y + 6 = \frac{11}{8}(x + 6)
\]

3. **Distribute and simplify:**

\[
y + 6 = \frac{11}{8}x + \frac{11}{8} \cdot 6
\]
\[
y + 6 = \frac{11}{8}x + \frac{66}{8}
\]
\[
y + 6 = \frac{11}{8}x + \frac{33}{4}
\]

4. **Isolate \(y\):**

\[
y = \frac{11}{8}x + \frac{33}{4} - 6
\]
Since \(6\) can be written as \(\frac{24}{4}\):

\[
y = \frac{11}{8}x + \frac{33}{4} - \frac{24}{4}
\]
\[
y = \frac{11}{8}x + \frac{9}{4}
\]

So, the equation of the line passing through the points \((-6, -6)\) and \((2, 5)\) is:

\[
y = \frac{11}{8}x + \frac{9}{4}
\]