Write an equation for a line parallel to $$ y=-3 x+4 $$ and passing through the point $$ (1,-2) $$, $$ y=\square $$ Question Help: Video Submit Question

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To find the equation of a line that is parallel to the given line $$ y = -3x + 4 $$ and passes through the point $$ (1, -2) $$, we can follow these steps:

1. **Identify the slope of the given line**: The slope-intercept form of a line is given by $$ y = mx + b $$, where $$ m $$ is the slope. From the equation $$ y = -3x + 4 $$, we can see that the slope $$ m $$ is $$-3$$.

2. **Use the same slope for the parallel line**: Since parallel lines have the same slope, the slope of our new line will also be $$-3$$.

3. **Use the point-slope form of the equation**: The point-slope form of a line 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. Here, $$ (x_1, y_1) = (1, -2) $$ and $$ m = -3 $$.

4. **Substitute the values into the point-slope form**:
   $$
   y - (-2) = -3(x - 1)
   $$

5. **Simplify the equation**:
   $$
   y + 2 = -3(x - 1)
   $$
   $$
   y + 2 = -3x + 3
   $$
   $$
   y = -3x + 3 - 2
   $$
   $$
   y = -3x + 1
   $$

Thus, the equation of the line parallel to $$ y = -3x + 4 $$ and passing through the point $$ (1, -2) $$ is:
$$
y = -3x + 1
$$

So, the final answer is:
$$
y = -3x + 1
$$
$$ y = -3x + 1 $$

Write an equation for a line parallel to \( y=-3 x+4 \) and passing through the point \( (1,-2) \), \( y=\square \) Question Help: Video Submit Question

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