Question

Use the points (2, 3) and (-1, -5), and the slope of 8/3, and write an equation in slope intercept form

Answer 1

To write the equation of a line in slope-intercept form (y = mx + b) given a slope \( m \) and a point \((x_1, y_1)\), we can use the point-slope form of the equation, which is:

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

Given:

- Slope \( m = \frac{8}{3} \)
- Point \( (x_1, y_1) = (2, 3) \)

Substituting these values into the point-slope formula:

\[
y - 3 = \frac{8}{3}(x - 2)
\]

Now, simplify this equation:

1. Distribute the slope on the right side:

\[
y - 3 = \frac{8}{3}x - \frac{16}{3}
\]

2. Add 3 to both sides to solve for \( y \):

\[
y = \frac{8}{3}x - \frac{16}{3} + 3
\]

3. Convert 3 into a fraction with a denominator of 3:

\[
3 = \frac{9}{3}
\]

So,

\[
y = \frac{8}{3}x - \frac{16}{3} + \frac{9}{3}
\]

4. Combine the constant terms:

\[
y = \frac{8}{3}x - \frac{7}{3}
\]

Thus, the equation of the line in slope-intercept form is:

\[
y = \frac{8}{3}x - \frac{7}{3}
\]