SOLUTION: how do i find the equation for 3/4(6,-1)

Algebra ->  Linear-equations -> SOLUTION: how do i find the equation for 3/4(6,-1)      Log On


   

Question 223752: how do i find the equation for 3/4(6,-1)
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
how do i find the equation for 3/4 (6,-1)

Here, I assume you meant the slope is 3%2F4 passing through the point (6,-1)

Write an equation for the line described as slope m=3%2F4 and passes through (6,-1). Write equation in slope-intercept form.

Step 1. The slope-intercept form is given as y=mx+b where m is the slope and b is the y-intercept b at x=0 or point (0,b). Here, the slope m=3/4.

Step 2. The slope m is given as

m=%28y2-y1%29%2F%28x2-x1%29

Step 3. Let (x1,y1)=(6,-1) or x1=6 and y1=-1. Let other point be (x2,y2)=(x,y) or x2=x and y2=y.

Step 4. Now we're given m=3%2F4. Substituting above values and variables in the slope equation m yields the following steps:

m=%28y2-y1%29%2F%28x2-x1%29

3%2F4=%28y-%28-1%29%29%2F%28x-6%29

Step 5. Multiply (x-6) to both sides to get rid of denominators on both sides of equation.

%28x-8%29%2A%283%2F4%29=%28x-6%29%28y%2B1%29%2F%28x-6%29

3x%2F4-8%2A3%2F4=y%2B1

3x%2F4-6=y%2B1

Step 6. Now add -1 to both sides of equation to solve for y.

3x%2F4-6%2B%28-1%29=y%2B1%2B%28-1%29

3x%2F4-7=y


Step 7. ANSWER: The equation is y=3x%2F4-7

Here's a graph below and note the slope and y-intercept at x=0 or point (0,-7) and the x-intercept at y=0 or at point (51/3, 0)and note it is consistent with the equation when substituting these

graph%28500%2C500%2C+-10%2C20%2C-15%2C5%2C+3x%2F4-7%29

Note: the above equation can be rewritten in standard form as

3x%2B5y=51

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J