How do I solve this?

Question

Write the slope-intercept form of the equation of the line through the given point with the given slope.

 

 

through:(-5,-5), slope=2/3

Answer 1

There is a formula, known as point slope formula, that churns out this answer quickly.  Normally you use subscripts to write it, but I don't see anything in the character set that resembles that.

 

if you were reading the formula aloud, you would say "y minus y sub zero equals the slope times the difference of x and x sub zero."

 

y - (-5) = (2/3) [x - (-5)]

y + 5 = 2/3 x + 10/3

y = 2/3 x + 10/3 - 5 

y = 2/3 x - 5/3

 

 

The other method  is to substitute the known values into the generic form of the slope intercept equation and solve for b.

y = mx + b

(-5) = 2/3 (-5) + b

-5 = -10/3 + b

-5 + 10/3 = b

-5/3 = b

therefore

y = 2/3 x - 5/3

 

Answer 2

Hi, Juliana,

      Slope-intercept form= y=mx+b       Slope= 2/3    (-5,-5)=(X,Y)      X=-5, Y=-5

Now substitute into the formula above all that you know.  However, the "b" is missing.

 

-5 = (2/3)(-5) +b  Solve for "b."  Get "b" by itself on the right side of equation.

 

-5 = -10/3   + b        Add +10/3 to both sides of the equation.

 

-5+10/3 = 10/3 - 10/3   +  b  Simplify.

 

-5 + 10/3  = b      Change -5  into 3rds by multiplying the numerator and denominator by 3/3.  -5(3)/1(3)

 

-15/3   + 10/3 =b             (-15+ 10)/3  =b    I will let you finish the problem. 

 

If you have further questions, let me know.  If I have helped you, please give me a thumbs up.

                                                             Susan C.