What is the x-intercept of the graph of the equation y = (2/5)x + 2?
Understand the Problem
The question is asking for the x-intercept of the equation y = (2/5)x + 2. To find the x-intercept, we need to set y to 0 and solve for x.
Answer
The x-intercept is \( x = -5 \).
Answer for screen readers
The x-intercept of the equation ( y = \frac{2}{5}x + 2 ) is ( x = -5 ).
Steps to Solve
- Set y to 0
Since we are looking for the x-intercept, we start by setting ( y = 0 ) in the given equation.
The equation is: $$ 0 = \frac{2}{5}x + 2 $$
- Rearrange the equation
Next, we want to isolate ( x ). To do this, we can start by subtracting 2 from both sides:
$$ -2 = \frac{2}{5}x $$
- Solve for x
To get ( x ) by itself, we will multiply both sides by the reciprocal of ( \frac{2}{5} ), which is ( \frac{5}{2} ):
$$ x = -2 \cdot \frac{5}{2} $$
- Calculate the final answer
Now, we just need to do the multiplication:
$$ x = -5 $$
The x-intercept of the equation ( y = \frac{2}{5}x + 2 ) is ( x = -5 ).
More Information
The x-intercept is the point where the line crosses the x-axis, which represents the value of ( x ) when ( y = 0 ). In this case, the x-intercept is at the coordinate (-5, 0).
Tips
- Forgetting to set ( y = 0 ).
- Not correctly isolating ( x ) during the rearranging of the equation.
- Confusing the signs when calculating the final answer.
