Question

Transform
4
x
+
−
5
y
=
−
9
4x+−5y=−9 into slope-intercept form (
y
=
m
x
+
b
y=mx+b ).

Answer 1

To transform the equation \( 4x - 5y = -9 \) into slope-intercept form (\( y = mx + b \)), we need to solve for \( y \).

Here's how we do that step by step:

1. Start with the original equation:
\[
4x - 5y = -9
\]

2. Isolate the term involving \( y \) by moving \( 4x \) to the other side:
\[
-5y = -4x - 9
\]

3. Divide every term by -5 to solve for \( y \):
\[
y = \frac{-4x}{-5} - \frac{9}{-5}
\]
This simplifies to:
\[
y = \frac{4}{5}x + \frac{9}{5}
\]

Now, the equation is in slope-intercept form, where:
- The slope \( m \) is \( \frac{4}{5} \),
- The y-intercept \( b \) is \( \frac{9}{5} \).

So, the final result is:
\[
y = \frac{4}{5}x + \frac{9}{5}
\]