Transform the following equations to the form y = mx + b: 1) 3x - y = -6 2) -2x + y = 10
Understand the Problem
The image contains two math problems. The first problem requires transforming the equation 3x - y = -6 into slope-intercept form (y = mx + b). The second problem involves solving the equation -2x + y = 10 for y to express it in slope-intercept form as well.
Answer
$y = 3x + 6$ $y = 2x + 10$
Answer for screen readers
$y = 3x + 6$ $y = 2x + 10$
Steps to Solve
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Isolate y in the first equation We want to get $y$ by itself on one side of the equation. Starting with $3x - y = -6$, subtract $3x$ from both sides: $3x - y - 3x = -6 - 3x$ $-y = -3x - 6$ Multiply both sides by $-1$ to solve for $y$: $(-1) * (-y) = (-1) * (-3x - 6)$ $y = 3x + 6$
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Isolate y in the second equation We want to isolate $y$ in the second equation $-2x + y = 10$. Add $2x$ to both sides of the equation: $-2x + y + 2x = 10 + 2x$ $y = 2x + 10$
$y = 3x + 6$ $y = 2x + 10$
More Information
Slope intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
Tips
A common mistake is forgetting to multiply every term by -1 when isolating $y$ in the first equation. For example, students may get $-y = -3x - 6$ and incorrectly change it to $y = -3x + 6$ or $y = -3x -6$ instead of $y = 3x + 6$.
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