Put the following equation of a line into slope-intercept form, simplifying all fractions: 9x + 6y = 42

Understand the Problem

The question is asking to rearrange the given equation of a line into slope-intercept form (y = mx + b), which involves solving for y and simplifying the fractions.

Answer

$y = -\frac{3}{2}x + 7$

Steps to Solve

Isolate y on one side of the equation

Start with the original equation (9x + 6y = 42). To isolate (y), we need to move the (9x) term to the other side.

Subtract (9x) from both sides:

$$ 6y = 42 - 9x $$

Simplify the equation

Now, divide every term by (6) to solve for (y):

$$ y = \frac{42}{6} - \frac{9x}{6} $$

This simplifies to:

$$ y = 7 - \frac{3}{2}x $$

Rearrange to slope-intercept form

To express it in slope-intercept form (y = mx + b), we rewrite the equation:

$$ y = -\frac{3}{2}x + 7 $$

Now the equation is in the slope-intercept form.

The slope-intercept form of the equation is

$$ y = -\frac{3}{2}x + 7 $$

More Information

In this equation, the slope (m) is (-\frac{3}{2}) and the y-intercept (b) is (7). The slope indicates that for every 2 units you move to the right along the x-axis, you move 3 units down along the y-axis.

Tips

Forgetting to keep track of the signs: Ensure to subtract correctly when moving terms across.
Not simplifying fractions properly: Always break down fractions to their simplest form.

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