Put the following equation of a line into slope-intercept form, simplifying all fractions. 4x - 3y = 9.
Understand the Problem
The question is asking to convert the equation of a line given in standard form (4x - 3y = 9) into slope-intercept form (y = mx + b), while simplifying any fractions that may arise in the process.
Answer
The equation in slope-intercept form is: $$ y = \frac{4}{3}x - 3 $$
Answer for screen readers
The slope-intercept form of the equation is:
$$ y = \frac{4}{3}x - 3 $$
Steps to Solve
- Isolate $y$ on one side of the equation
To convert the equation from standard form to slope-intercept form, the first step is to isolate $y$ on one side.
Starting with the equation: $$ 4x - 3y = 9 $$
Subtract $4x$ from both sides: $$ -3y = -4x + 9 $$
- Divide by the coefficient of $y$
Next, we need to get $y$ alone by dividing every term by $-3$: $$ y = \frac{4}{3}x - 3 $$
- Rewrite in slope-intercept form
Now the equation is in slope-intercept form, which is $y = mx + b$. Here, $m = \frac{4}{3}$ is the slope and $b = -3$ is the y-intercept.
The slope-intercept form of the equation is:
$$ y = \frac{4}{3}x - 3 $$
More Information
The slope-intercept form is often used in algebra because it readily provides the slope and y-intercept, making it easier to graph the equation. The slope $\frac{4}{3}$ indicates the line rises 4 units for every 3 units it runs to the right, while the y-intercept of $-3$ indicates where the line crosses the y-axis.
Tips
- Forgetting to change the sign of the terms when moving them across the equality.
- Not dividing every term by the coefficient of $y$, which results in an incorrect slope-intercept form.
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