The problem asks to find the equation of a line that is parallel to $y = -4x + 8$ and passes through the point $(1, 3)$.

Step 1: Identify the slope of the given line

The equation $y = -4x + 8$ is in slope-intercept form $y = mx + b$, where $m$ is the slope. From the equation, we can see that the slope $m = -4$.

Step 2: Slope of the parallel line

Parallel lines have the same slope, so the slope of the new line will also be $m = -4$.

Step 3: Use the point-slope form of the line equation

To find the equation of a line passing through the point $(1, 3)$ with slope $m = -4$, we use the point-slope form: $y - y_1 = m(x - x_1)$ Substitute $x_1 = 1$, $y_1 = 3$, and $m = -4$: $y - 3 = -4(x - 1)$

Step 4: Simplify the equation

Distribute the slope on the right side: $y - 3 = -4x + 4$ Add 3 to both sides to solve for $y$: $y = -4x + 7$

Thus, the equation of the line that is parallel to $y = -4x + 8$ and passes through the point $(1, 3)$ is: $y = -4x + 7$

Would you like any further clarifications or details?

Related Questions:

1. What is the slope-intercept form of a line?
2. How do you find the equation of a line passing through two points?
3. What is the difference between parallel and perpendicular lines?
4. How can you convert a line equation from point-slope to slope-intercept form?
5. How do you check if two lines are parallel?

Tip:

When working with parallel lines, always remember that they share the same slope.