Answer:
The equation of parallel line passes through the point (−4,−6 ) is:
y = -6
Please also check the attached graph.
Step-by-step explanation:
The slope-intercept form of the line equation
y = mx+b
where
Given that on a coordinate plane passes through (-8, 4) and (8, 4).
As the value of y remains the same for any value of x.
i.e. y = 4 for any value of x.
Thus, the given line is a horizontal line.
We know that the slope of a horizontal line is zero.
Also it is clear that at x = 0, the value of y = 4. In other words, we can observe that the y-intercept b = 4.
so substitutig m = 0 and b = 4 in the slope-intercept form
y = mx + b
y = 0x + 4
y = 4
Therefore, the equation of line passing through the point (-8, 4) and (8, 4) is:
y = 4
Now, we also know that the slope of parallel lines is equal.
Thus, the slope of the line parallel to the line y = 4 is also 0.
As the parallel line passes through (−4,−6 ).
so substituting m = 0 and (-4, -6) in the slope-intercept form of line equation to determine the y-intercept b
y = mx + b
(-6) = 0(-4) + b
-6 = 0 + b
switching the sides
0 + b = -6
b = -6
Thus, the slope-intercept b = -6
now substituting m = 0 and b = -6 in the slope-intercept form of line equation
y = mx + b
y = 0(x) + -6
y = 0 - 6
y = -6
Therefore, the equation of parallel line passes through the point (−4,−6 ) is:
y = -6
Please also check the attached graph.
