What the answer to 2,3 and y=x+4

Question

_{what is the answer to 2,3 and y=x+4 in the terms of parallel lines? Find the equation of line passing through the given point and parallel to the given equation.} 

Answer 1

Since the line is parallel it's slope is the same which is 1. 

 

Now let's work on the equation of the line:

 

y - 3 = 1 (x - 2)

 

y = x - 2 + 3

 

y = x + 1

 

That's the equation of your parallel line. 

Answer 2

Parallel lines have the same slope.  In the slope-intercept form of the equation of a line (y=mx+b), m=slope.

 

The given line is y=1*x+4    The slope is 1.

All parallel lines have the form y = 1*x + b,   so use point (2,3) to find b.

    3 = 2 + b

    1 = b             (subtract 2 from both sides)

The parallel line has the equation:  y=x+1

Answer 3

Hi Sophia,

 

First of all we must know that parallel lines have the same slope and the slope of the line whose equation is  y = x + 4 is 1 because the given equation is already in slope-intercept form( y = mx + b) where m is the slope. The line passing through the point whose coordinates of (2,3) and parallel to the line whose equation is y = x + 4 also has a slope of 1. Using the point-slope form of a linear equation (y - y₁) = m ( x-x₁) and substituting y₁ = 3, x₁ = 2 and m = 1 we get the equation 

      y - 3 = 1 (x - 2) or in slope intercept form   y = x + 1