Answer:
The equation of required line is: [tex]\mathbf{x+y=5}[/tex]
Step-by-step explanation:
We need to find an equation of the line that passes through the point (2,3) and is parallel to the line x+y=4
For finding an equation of line, we need to find slope and y-intercept of the line.
Finding slope:
If the lines are parallel their slope is same
We are given: x+y=4
Writing in slope-intercept form: [tex]y=mx+b[/tex] where m is slope and b is y-intercept
[tex]x+y=4\\y=-x+4[/tex]
Comparing [tex]y=-x+4[/tex] with [tex]y=mx+b[/tex] the slope m is -1
So, slope of given line is -1
It is parallel with required line, so they have same slope.
The slope of required line is m=-1
Finding y-intercept
Using slope m=-1 and point(2,3) we can find y-intercept
Using slope-intercept form: [tex]y=mx+b[/tex]
[tex]y=mx+b\\3=-1(2)+b\\3=-2+b\\b=3+2\\b=5[/tex]
So, y-intercept is: b=5
The equation of required line having slope m=-1 and y-intercept b = 5 is
[tex]y=mx+b\\y=-1x+5\\y=-x+5\\x+y=5[/tex]
So, equation of required line is: [tex]\mathbf{x+y=5}[/tex]
The equation of the line that passes through the point (2,3) and is parallel to the line x+y=4 is y = -x + 5
Two equations are parallel if they have equal slope
For the equation x + y = 4
Rewrite the equation in the form y = mx + c
y = -x + 4
Compare y = -x + 4 with y = mx + c
The slope, m = -1
The equation parallel to x + y = 4 will also have a slope, m = -1
The line passes through the point (2, 3)
That is, x₁ = 2, y₁ = 3
The point-slope form of the equation of a line is:
y - y₁ = m(x - x₁)
Substitute x₁ = 2, y₁ = 3 into y - y₁ = m(x - x₁)
y - 3 = -1(x - 2)
y - 3 = -x + 2
y = -x + 2 + 3
y = -x + 5
The equation of the line that passes through the point (2,3) and is parallel to the line x+y=4 is y = -x + 5
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