Find the equation of a line passing through the point `(1,-2)` and whose slope is `4`.

Answer

To find the equation of a line passing through the point (1, -2) with a slope of 4, we can use the point-slope form of the equation of a line. The point-slope form is given by:

\[ y - y_1 = m(x - x_1) \]

where \((x_1, y_1)\) is a point on the line and \(m\) is the slope.

### Step 1: Identify the point and slope
We have:
- Point \((x_1, y_1) = (1, -2)\)
- Slope \(m = 4\)

### Step 2: Substitute the values into the point-slope formula
Now, we substitute \(x_1\), \(y_1\), and \(m\) into the point-slope formula:

\[ y - (-2) = 4(x - 1) \]

### Step 3: Simplify the equation
This simplifies to:

\[ y + 2 = 4(x - 1) \]

Now, distribute the 4 on the right side:

\[ y + 2 = 4x - 4 \]

### Step 4: Isolate \(y\)
Next, we isolate \(y\) by subtracting 2 from both sides:

\[ y = 4x - 4 - 2 \]

This simplifies to:

\[ y = 4x - 6 \]

### Step 5: Rearranging to standard form (optional)
If we want to express this in standard form \(Ax + By + C = 0\), we can rearrange it:

\[ 4x - y - 6 = 0 \]

### Final Equation
Thus, the equation of the line in slope-intercept form is:

\[ y = 4x - 6 \]

Or in standard form:

\[ 4x - y - 6 = 0 \]

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