Here are some math problems that involve converting linear equations into the slope-intercept form, $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept:

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Problem 1:

Convert the following equation into slope-intercept form:

$2x + 3y = 12$

Solution:

1. Subtract $2x$ from both sides: $3y = -2x + 12$

2. Divide both sides by 3: $y = -\frac{2}{3}x + 4$

So, the equation in slope-intercept form is: $y = -\frac{2}{3}x + 4$

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Problem 2:

Convert the following equation into slope-intercept form:

$4x - 2y = 10$

Solution:

1. Subtract $4x$ from both sides: $-2y = -4x + 10$

2. Divide both sides by -2: $y = 2x - 5$

So, the equation in slope-intercept form is: $y = 2x - 5$

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Problem 3:

Convert the following equation into slope-intercept form:

$5y - 10x = 15$

Solution:

1. Add $10x$ to both sides: $5y = 10x + 15$

2. Divide both sides by 5: $y = 2x + 3$

So, the equation in slope-intercept form is: $y = 2x + 3$

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Problem 4:

Convert the following equation into slope-intercept form:

$6x + y = 8$

Solution:

1. Subtract $6x$ from both sides: $y = -6x + 8$

So, the equation in slope-intercept form is: $y = -6x + 8$

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Problem 5:

Convert the following equation into slope-intercept form:

$3x + 4y = -20$

Solution:

1. Subtract $3x$ from both sides: $4y = -3x - 20$

2. Divide both sides by 4: $y = -\frac{3}{4}x - 5$

So, the equation in slope-intercept form is: $y = -\frac{3}{4}x - 5$

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Would you like further details on any of these examples, or have any specific questions?

Relative Questions:

1. How do you find the slope when the equation is not in standard form?
2. What is the significance of the y-intercept in graphing?
3. How can you rewrite an equation if it has fractions in the slope?
4. What happens if both the slope and y-intercept are negative?
5. Can a vertical line equation be expressed in the form $y = mx + b$?

Tip:

Always isolate the $y$-term first when converting equations into slope-intercept form!