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
[tex]y = mx+b[/tex]
where
- [tex]m[/tex] is the slope
- [tex]b[/tex] is the y-intercept
Given the equation
[tex]y = x - 3[/tex]
comparing with the slope-intercept form of the line equation
Slope m = 1
Important Tip:
- 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
[tex]y = mx+b[/tex]
[tex]1 = 1(-2) + b[/tex] ∵ (x, y) = (-2, 1) and m = 1
[tex]1 = -2 + b[/tex]
switch sides
[tex]-2+b = 1[/tex]
add 2 to both sides
[tex]-2 + b + 2 = 1 + 2[/tex]
simplify
[tex]b = 3[/tex]
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
[tex]y = mx + b[/tex]
[tex]y = (1)x + 3[/tex]
[tex]y = x + 3[/tex]
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.
