What is an equation of the line that passes through the point (2,3) and is parallel to the line x+y=4

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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The equation of required line is:

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: where m is slope and b is y-intercept

Comparing with 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:

So, y-intercept is: b=5

The equation of required line having slope m=-1 and y-intercept b = 5 is

So, equation of required line is:

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Step-by-step explanation:

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