The intercepts made by the plane `2x-3y+5z+4=0` on the coordinate exes are `-2, (4)/(3) and - (4)/(5).`

Answer

To determine whether the intercepts made by the plane \(2x - 3y + 5z + 4 = 0\) on the coordinate axes are \(-2\), \(\frac{4}{3}\), and \(-\frac{4}{5}\), we will follow these steps:

### Step 1: Rewrite the Plane Equation
Start with the given equation of the plane:
\[ 2x - 3y + 5z + 4 = 0 \]
Rearranging gives:
\[ 2x - 3y + 5z = -4 \]

### Step 2: Convert to Intercept Form
To express this in intercept form, we will isolate the variables. Multiply the entire equation by \(-1\) to make the right side positive:
\[ -2x + 3y - 5z = 4 \]
Now, divide the entire equation by \(4\):
\[ \frac{-2x}{4} + \frac{3y}{4} - \frac{5z}{4} = 1 \]
This simplifies to:
\[ \frac{x}{-2} + \frac{y}{\frac{4}{3}} + \frac{z}{-\frac{4}{5}} = 1 \]

### Step 3: Identify the Intercepts
From the equation in intercept form:
\[ \frac{x}{-2} + \frac{y}{\frac{4}{3}} + \frac{z}{-\frac{4}{5}} = 1 \]
We can identify the intercepts:
- The x-intercept \(a = -2\)
- The y-intercept \(b = \frac{4}{3}\)
- The z-intercept \(c = -\frac{4}{5}\)

### Step 4: Conclusion
The intercepts we found are:
- x-intercept: \(-2\)
- y-intercept: \(\frac{4}{3}\)
- z-intercept: \(-\frac{4}{5}\)

These match the intercepts given in the question, confirming that the statement is **true**.