Slope questions, easy 10 points?

Question

Please help me with these two problems below.

Write an equation of the line described:

1. The line with y-intercept 4 and x-intercept -2.

2. The line through (-1,4) and (5,8)

Thank you.

Answer 1

You may use the Point-slope formula: Y- y1 = m(X-x1)  

   such that m = slope.

Now, if the straight line has 4 as its y-intercept, what is the corresponding x-coordinate? Remember, points come in pairs. (x,y). If you said x=0 then you got it right. So, label this point A(x1,y1) --> A(0,4).

Next, the x-intercept is -2. Again, what is the corresponding y-coordinate?  Alright, if you guessed 0 then you are on the right track! So, let us label this point as point B(x2,y2) --> B(-2,0).

Remember, you need to find the slope first.

   m =  (y2 - y1)/(x2-x1)      ----> Rise over Run  :)

   m  =  (0-4)/(-2-0)  =  -4/-2  = 2  (Review rules on subtracting and     dividing signed numbers)

Now, you are ready to substitute the needed values in the first equation.  

                  Y-y1 = m(X-x1)          

**** You may pick either point A or point B to substitute for your (x1,y1). You will get the same result either way.  I usually pick point A because I have already labeled it as A(x1,y1).

So:    Y - 4 = 2(X-0)    

         Y - 4 = 2X              ----->  Add 4 to both sides of the equation

         Y - 4 + 4 = 2X + 4   ----->  Addition Property of Equality

          Y = 2X + 4            ------> Slope-intercept form of a line

Do the next problem by labeling the points first then solving for the slope. After that, use the point-slope form of the line then simplify to get the slope-intercept form of the line.

Okay. I hope this helped.

    

Answer 2

Equation of straight line in intercept form is y = mx + c

                                                             => y = 4x - 2

The line passing through (-1,4) and (5,8) is

Slope =  (8-4) / {5 - (-1)} = 4/6 = 2/3

Intercept = 8 - 2/3 * 5 = 8 - 10/3 = 14/3

So equation is y = 2/3 x + 14/ 3

                => 3y = 2x + 14

Answer 3

1. use the 2 points (0,4) and (-2,0) to find the slope

    m=(y2-y1)/(x2-x1)

       =(0-4)/(-2-0)

       =(-4)/(-2)

       =2

The y-intercept is already given

the equation of the line is y=2x+4

2. Find the slope from the points (-1,4) and (5,8)

m=(y2-y1)/(x2-x1)

   =(8-4)/(5-(-1))

   =4/6

   =2/3

find the y-intercept by subbing the slope and either point into the equation y=mx+b

4=(2/3)(-1)+b

4=(-2)/3+b

b=14/3

so the equation is y=2/3x+14/3

Answer 4

1)   y=2x +4

2)   3y=2x +14