Write an equation in slope-intercept form given 5x - 4y = -12.
Understand the Problem
The question is asking to rearrange the equation 5x - 4y = -12 into slope-intercept form, which is y = mx + b. The user is required to express the equation correctly using specified formatting for fractions.
Answer
The equation in slope-intercept form is $$ y = \frac{5}{4}x + 3 $$
Answer for screen readers
The equation in slope-intercept form is
$$ y = \frac{5}{4}x + 3 $$
Steps to Solve
- Isolate the term with y
To rearrange the equation $5x - 4y = -12$, we first isolate the $y$ term by moving $5x$ to the right side of the equation.
[ -4y = -5x - 12 ]
- Divide by the coefficient of y
Next, we divide every term in the equation by $-4$ to solve for $y$.
[ y = \frac{-5x}{-4} + \frac{-12}{-4} ]
- Simplify the fractions
Now we simplify the fractions:
[ y = \frac{5}{4}x + 3 ]
The equation is now in slope-intercept form.
The equation in slope-intercept form is
$$ y = \frac{5}{4}x + 3 $$
More Information
In slope-intercept form $y = mx + b$, $m$ represents the slope and $b$ represents the y-intercept. Here, the slope is $\frac{5}{4}$, and the y-intercept is $3$.
Tips
- Not isolating y correctly: Beginners may forget to move all terms to one side before isolating $y$.
- Mistakes in dividing by negative numbers: Be careful with signs when dividing by a negative coefficient.
