Question

convert and write the equation in slope intercept form. y-3=5/3(x-3)

Answer 1

To convert the equation \( y - 3 = \frac{5}{3}(x - 3) \) into slope-intercept form (which is \( y = mx + b \)), follow these steps:

1. Distribute \(\frac{5}{3}\) on the right side:
\[
y - 3 = \frac{5}{3}x - \frac{5}{3} \cdot 3
\]
This simplifies to:
\[
y - 3 = \frac{5}{3}x - 5
\]

2. Next, add 3 to both sides:
\[
y = \frac{5}{3}x - 5 + 3
\]
Simplifying further:
\[
y = \frac{5}{3}x - 2
\]

Now, the equation in slope-intercept form is:
\[
y = \frac{5}{3}x - 2
\]

Here, the slope \(m\) is \(\frac{5}{3}\) and the y-intercept \(b\) is \(-2\).