Answer the following two questions. What is the main difference between the two?
1 answer:
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Answer:
The equation of a line parallel to y = x - 3 that contains the point (-2, 1) is:
The graph of both the parallel equation is shown below to make you further understand the concept.
Step-by-step explanation:
The slope-intercept form of the line equation
where
is the slope
is the y-intercept
Given the equation
comparing with the slope-intercept form of the line equation
Slope m = 1
<u>Important Tip:</u>
- As the parallel lines never intersect, therefore, they have the same slopes.
Thus, the slope of the parallel line is also 1.
As the parallel line contains the point (-2, 1).
so substitute m = 1 and (-2, 1) in the slope-intercept form of the line equation to determine the y-intercept of the parallel line
∵ (x, y) = (-2, 1) and m = 1
switch sides
add 2 to both sides
simplify
Thus, the y-intercept b of the parallel line is: b = 3
now substitute b = 3 and m = 1 in the slope-intercept form of the line equation to determine the equation of the parallel line
Therefore, the equation of a line parallel to y = x - 3 that contains the point (-2, 1) is:
The graph of both the parallel equation is shown below to make you further understand the concept.
From the graph:
- The green line represents the equation y = x - 3
- The black line represents the parallel equation y = x + 3
It is clear that both lines are parallel.
