The question asks to determine the slope-intercept form of the equation of a line that is parallel to $y = -\frac{3}{4}x + 1$ and passes through the point $(-4, 2)$.

Step 1: Identify the slope of the parallel line

Since the line must be parallel to $y = -\frac{3}{4}x + 1$, it will have the same slope. The slope $m$ is $-\frac{3}{4}$.

Step 2: Use the point-slope form

To find the equation of the line, use the point-slope form of a line equation: $y - y_1 = m(x - x_1)$ where $(x_1, y_1) = (-4, 2)$ is the point the line passes through, and $m = -\frac{3}{4}$.

Substitute the values: $y - 2 = -\frac{3}{4}(x + 4)$

Step 3: Solve for $y$ (convert to slope-intercept form)

Simplify the equation: $y - 2 = -\frac{3}{4}x - 3$ Add 2 to both sides: $y = -\frac{3}{4}x - 3 + 2$ $y = -\frac{3}{4}x - 1$

Final Equation

The slope-intercept form of the line is: $y = -\frac{3}{4}x - 1$

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Relative Questions:

1. What is the difference between point-slope form and slope-intercept form?
2. How do you find the slope of a line from its equation?
3. What does it mean for two lines to be parallel in terms of their slopes?
4. How do you convert from point-slope form to slope-intercept form?
5. Can this method be applied to perpendicular lines as well? How?

Tip:

When dealing with parallel lines, remember that they always share the same slope!