AI Math Solver
Resources
Questions
Pricing
Login
Register
Home
>
Questions
>
Rewrite $x - 4y = 4$ into Slope-Intercept Form (Algebra 1 Practice)
Mathematics
High School Grade 9 (Algebra 1)
Question Content
Put the equation $x - 4y = 4$ in Slope Intercept form. Show all steps Algebraically.
Correct Answer
$y = \\frac{1}{4}x - 1$
Detailed Solution Steps
1
Step 1: Recall that slope-intercept form is defined as $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. Our goal is to isolate $y$ on one side of the equation.
2
Step 2: Subtract $x$ from both sides of the original equation to get the term with $y$ alone: $-4y = -x + 4$.
3
Step 3: Divide every term in the equation by $-4$ to solve for $y$: $y = \\frac{-x}{-4} + \\frac{4}{-4}$.
4
Step 4: Simplify the fractions to get the final slope-intercept form: $y = \\frac{1}{4}x - 1$.
Knowledge Points Involved
1
Slope-Intercept Form of a Linear Equation
The slope-intercept form is written as $y = mx + b$, where $m$ represents the slope (rate of change of the line) and $b$ represents the y-intercept (the point where the line crosses the y-axis). This form is used to easily graph linear equations and identify key characteristics of the line.
2
Solving Linear Equations for a Specified Variable
To isolate a variable (in this case $y$), use inverse operations: subtract or add terms to move them to the opposite side of the equation, then multiply or divide to solve for the target variable. Apply operations to all terms on both sides to maintain equality.
Loading solution...
