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Rewrite $2y = 3x - 10$ into Slope-Intercept Form (Algebra 1)
Mathematics
High School Grade 9 (Algebra 1)
Question Content
Put the equation $2y = 3x - 10$ in Slope Intercept form. Show all steps Algebraically.
Correct Answer
$y = \\frac{3}{2}x - 5$
Detailed Solution Steps
1
Step 1: Recall slope-intercept form is $y = mx + b$, so we need to isolate $y$.
2
Step 2: Divide every term in the equation by $2$ to solve for $y$: $y = \\frac{3x}{2} - \\frac{10}{2}$.
3
Step 3: Simplify the constant term to get the final form: $y = \\frac{3}{2}x - 5$.
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.
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