The equation of the line which passes through the point (-1, 2) and is parallel to the line y = x + 4 is y = x + 3
Gtiven that line passes through the point (-1, 2) and parallel to line y = x + 4
We have to find the equation of line
The equation of line in slope intercept form is given as:
y = mx + c ---------- eqn 1
where "m" is the slope of line and "c" is the y - intercept
Let us first find the slope of line
Given equation of line is y = x + 4
On comparing the given equation of line y = x + 4 with general slope intercept form y = mx + c,
we get slope of line "m" = 1
We know that slopes of parallel lines are equal
So the slope of line parallel to line having equation y = x + 4 is also 1
Now we have to find the equation of line having slope "m" = 1 and passes through point (-1, 2)
Substitute m = 1 and (x, y) = (-1, 2) in eqn 1
2 = 1(-1) + c
2 = -1 + c
c = 3
Thus the required equation of line is:
Substitute c = 3 and m = 1 in eqn 1
y = 1x + 3
y = x + 3
Thus the required equation of line is found out
The equation of line for point [tex](-1,2)[/tex] can be determine by general equation of line.
The equation of line for point [tex](-1,2)[/tex] is [tex]y=x+3[/tex].
Given:
The line is parallel to line [tex]y=x+4[/tex].
The line passes through the point [tex](-1,2)[/tex].
Write the general equation for line.
[tex]y=mx+c[/tex]-------------------------- (1)
Here, [tex]m[/tex] is slope and [tex]c[/tex] is y-intercept.
Write the given line equation.
[tex]y=x+4[/tex]-----------------------------(2)
On comparing equation (1) and (2) we get,
[tex]m=1\\c=4[/tex]
As per the definition of line, parallel line has equal slope.
Substitute [tex]m=1[/tex], [tex]x=-1[/tex] and [tex]y=2[/tex] for the given point [tex](-1,2)[/tex] in equation (1).
[tex]2 = 1(-1) + c2 = -1 + cc = 3[/tex]
Write the equation of line from the above value.
[tex]y=1\times x+3\\y=x+3[/tex]
Thus, the equation of line for point [tex](-1,2)[/tex] is [tex]y=x+3[/tex].
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