Slope/intercepts

Question

Find the equations of the following lines in slope/intercept form:

A) horizontal and passing through the point (6, -2)
B) parallel to y=2x+3 and passing through the point (5, 7)
C) passing through the points (-3, 5) and (2, 5)

Answer 1

Greg,

 

(A) The slope of any horizontal line is always 0.  So, the slope-intercept form of the equation for this line would be:

 

y = 0x + b or y = b.  b is the y-intercept.  Since the line goes through the point (6, -2), we know that for every point on the line (x, y), the y value will always be -2 (including where it crosses the y-axis).  The equation of this line then is:

 

y = -2

 

(B) Any line parallel to y = 2x + 3 will have the same slope and will be in the form:

 

y = 2x + b

 

To find b, substitute the coordinates for the point we know is on the line (5, 7) into this equation:

 

7 = 2(5) + b

 

7 = 10 + b

 

-3 = b

 

The equation for this line then is:

 

y = 2x - 3

 

(C)  The general form of the equation of a line passing through any point is:

 

y - y₁ = m(x - x₁) where m is the slope and (x₁, y₁) is a point on the line.

 

We need to find the slope first.  

 

m = (y₂ - y₁)/(x₂ - x₁); rise/run

 

m = (5 - 5)/(2 - (-3))

 

m = 0/5 = 0  the slope is zero.

 

Then the equation of this line is:

 

y - 5 = 0(x - (-3))

 

y - 5 = 0

 

y = 5

 

If you look at the two points given, you'll note that both y-values are the same => the line is horizontal => slope is zero.

Answer 2

(A)

     Horizontal line that passes through (6, -2).  For horizontal lines, y has a constant value.

     Equation is:  

              y = -2 

 

(B) 

      Parallel lines have the same slope,  The given equation is in slope-intercept form (y=mx+b).

      m = the slope, so the sloppe of our line is 2.

 

      Our line passes through (5,7).  We can use the point=slope formula to find the equation.

      

          y - y₁ = m(x - x₁)

          y - 7  = 2(x - 5)

          y - 7  = 2x - 10

          y = 2x - 10 + 7

          y = 2x - 3

 

(C)

       The slope of the line passing through (-3,5) and (2,5) is 0, because the y-values are constant.  the slope is 0

        Equation of the line is:

 

            y = 5