slope intercept form

Question

I don't understand how to write in slope intercept form.

 

Find the equation for a line which passes through the points (2,9) and (4,-1). Write the equation in slope-intercept form. (Show Work)

Answer 1

Hi Jeff,

 

Let's begin by writing the slope-intercept form of a linear equation:

    y = mx + b (m is slope and b is y-intercept)

 

From the above equation, we see that we need two things in order to write our equation:

    1.  The slope (m).

    2.  The y-intercept (b), the value for y when x=0.

 

We can determine the slope (m) of a line if we know two of its points.  It's the difference in the y coordinates of the two points divided by the difference in the x coordinates of the two points:

    m = (y₂ - y₁) / (x₂ - x₁)

           (x₁,y₁) = (2,9) - our 1st given point

           (x₂,y₂) = (4,-1) - our 2nd given point

    m = (-1 - 9) / (4 - 2)

    m = -10/2

    m = -5 (slope of line)

 

We can determine the y-intercept (b) by plugging in the coordinates of a point (x,y) on the line and it's slope (m) and solving for b:

    y = mx + b (slope-intercept form)

          m = -5 (determined above)

          (x,y) = (4,-1):  our 2nd given point

                               (easier numbers for calculation)

   -1 = -5(4) + b

   -1 = -20 + b

    b = -1 + 20

    b = 19 (y-intercept)

 

Now we have everything we need to write the slope-intercept form of the equation for our line:

    y = mx + b

          m = -5 (determined above)

          b = 19 (determined above)

    y = -5x + 19 (equation in slope-intercept form)

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.

Answer 2

First of all the slope intercept form is the following equation for a line:    Y= mX  +b, where m =slope and 

 

b=y-intercept, where the line crosses the y-axis.

 

 

Find the slope by using the two points that they gave you: 

 

1.  Call the first point (X_1,Y_{1)=(2,9)  and    (X sub 1, Y sub 1).}

 

2.  Call the second point given (X₂,Y₂)= (4,-1).

 

3.  Use slope equation to find the line's slope:   slope=m= (Y₂-Y₁)/(X₂-X₁)

 

4.  Substitute into the slope equation:   (-1-9)/ (4-2)  =  -10/ 2  = -5= slope of line.

 

5.  Now substitute into the slope-intercept equation to find the value for "b."      

 

Try the point (4,-1):      y=mx +b             -1= -5(4)  +b

 

-1= -20 + b

 

6.  solve for "b."        -1+20 = b                 19=b= y-intercept

 

7.  Write the equation using all the information that you have now:   Change  y=mX +b  to    y= -5X+ 19 (Answer) .

 

8.  This means that the line crosses the y-axis when X=0 and y=19.  Also, the line has a negative slope, which means that it moves to the right on the graph.