Change the statement from standard form to slope-intercept form. Identify the slope and y-intercept

Question

10x-5y=15

Answer 1

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

Given the equation: \[ 10x - 5y = 15 \]

Let's isolate \( y \):

1. Subtract \( 10x \) from both sides: \[ -5y = -10x + 15 \]

2. Now divide every term by \(-5\) to solve for \( y \): \[ y = \frac{-10}{-5}x + \frac{15}{-5} \] \[ y = 2x - 3 \]

Now, the equation is in slope-intercept form \( y = mx + b \).

From the equation \( y = 2x - 3 \):

• The slope \( m \) is \( 2 \).
• The y-intercept \( b \) is \( -3 \).

So, the slope is \( 2 \) and the y-intercept is \( -3 \).