Find equation of straight line through $$ (-1,4) $$ and perpendicular to the line passing through $$ (3,0) $$ and $$ (1,-2) $$.

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To find the equation of the straight line that passes through the point $$(-1, 4)$$ and is perpendicular to the line passing through the points $$(3, 0)$$ and $$(1, -2)$$, follow these steps:

### 1. Find the Slope of the Given Line

First, determine the slope ($$m_1$$) of the line passing through $$(3, 0)$$ and $$(1, -2)$$:

$$
m_1 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - 0}{1 - 3} = \frac{-2}{-2} = 1
$$

### 2. Determine the Slope of the Perpendicular Line

The slope of a line perpendicular to another is the negative reciprocal of the original slope. Thus, the slope ($$m_2$$) of the perpendicular line is:

$$
m_2 = -\frac{1}{m_1} = -\frac{1}{1} = -1
$$

### 3. Use the Point-Slope Form to Find the Equation

With the slope $$m_2 = -1$$ and passing through the point $$(-1, 4)$$, use the point-slope formula:

$$
y - y_1 = m(x - x_1)
$$

Substituting the known values:

$$
y - 4 = -1(x - (-1)) \
y - 4 = -1(x + 1) \
y - 4 = -x - 1 \
$$

### 4. Simplify to the Slope-Intercept Form

Solve for $$y$$:

$$
y = -x - 1 + 4 \
y = -x + 3
$$

### Final Equation

$$
\boxed{y = -x + 3}
$$
The equation of the line is $$ y = -x + 3 $$.

Find equation of straight line through
and perpendicular to the line
passing through and .

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Find equation of straight line through and perpendicular to the line passing through and .