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 $.

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.

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