writing linear eqautions from standard form to slope-intercept form

Question

4x-5y=40

Answer 1

To convert the linear equation from standard form \( Ax + By = C \) to slope-intercept form \( y = mx + b \), we need to solve for \( y \).

Starting with the equation:

\[ 4x - 5y = 40 \]

1. Isolate the term with \( y \) by subtracting \( 4x \) from both sides:

\[ -5y = -4x + 40 \]

2. Next, divide every term by \(-5\) to solve for \( y \):

\[ y = \frac{4}{5}x - 8 \]

Now, the equation \( y = \frac{4}{5}x - 8 \) is in slope-intercept form, where:

• The slope \( m \) is \( \frac{4}{5} \)
• The y-intercept \( b \) is \( -8 \)