Questions: Rewrite the following equation in slope-intercept form. y+5=6(x-4) Write your answer using integers, proper fractions, and improper fractions in simplest form.

$Rewrite the following equation in slope-intercept form. y+5=6(x-4) Write your answer using integers, proper fractions, and improper fractions in simplest form.$

Transcript text: Rewrite the following equation in slope-intercept form. \[ y+5=6(x-4) \] Write your answer using integers, proper fractions, and improper fractions in simplest form.

Solution

Solution Steps

To rewrite the given equation in slope-intercept form, we need to solve for $ y $. The slope-intercept form of a linear equation is $ y = mx + b $, where $ m $ is the slope and $ b $ is the y-intercept. Start by distributing the 6 on the right side of the equation, then isolate $ y $ by moving other terms to the right side.

Step 1: Rewrite the Original Equation

We start with the equation given in the problem: \[ y + 5 = 6(x - 4) \]

Step 2: Distribute on the Right Side

Next, we distribute the $6$ on the right side: \[ y + 5 = 6x - 24 \]

Step 3: Isolate $y$

To isolate $y$, we subtract $5$ from both sides: \[ y = 6x - 24 - 5 \] This simplifies to: \[ y = 6x - 29 \]