Question

writing equations of parallel lines
what is the slope of the line that is parallel to the given line and passes through the given point?
-4
-1/4
1/4
4
the equation, in point - slope form, of the line that parallel to the given line and passes through the point?
the y - intercept of the line that is parallel to the ne and passes through the given point?

Explanation:

Step1: Calculate slope of given line

Use points $(-6, 8)$ and $(2, 6)$:
$$m = \frac{6-8}{2-(-6)} = \frac{-2}{8} = -\frac{1}{4}$$

Step2: Parallel lines have equal slope

Parallel line slope = $-\frac{1}{4}$

Step3: Identify target point

Given point is $(-2, -4)$

Step4: Write point-slope form

Point-slope formula: $y-y_1=m(x-x_1)$
$$y - (-4) = -\frac{1}{4}(x - (-2))$$
Simplify: $y + 4 = -\frac{1}{4}(x + 2)$

Step5: Find y-intercept

Rewrite to slope-intercept form $y=mx+b$:
$$y = -\frac{1}{4}x - \frac{1}{2} - 4$$
$$y = -\frac{1}{4}x - \frac{9}{2}$$
So $b = -\frac{9}{2} = -4.5$

Answer:

1. Slope of the parallel line: $-\frac{1}{4}$
2. Point-slope form equation: $y + 4 = -\frac{1}{4}(x + 2)$
3. y-intercept of the parallel line: $-\frac{9}{2}$ (or $-4.5$)