SOLUTION: 1. A line passes through (2, –1) and (8, 4). a. Write an equation for the line in point-slope form. b. Rewrite the equation in standard form using integers.

Algebra ->  Algebra  -> Linear-equations -> SOLUTION: 1. A line passes through (2, –1) and (8, 4). a. Write an equation for the line in point-slope form. b. Rewrite the equation in standard form using integers.       Log On

Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 240679: 1. A line passes through (2, –1) and (8, 4).
a. Write an equation for the line in point-slope form.
b. Rewrite the equation in standard form using integers.
Answer by ankor@dixie-net.com(12701) About Me  (Show Source):
You can put this solution on YOUR website!
1. A line passes through (2, –1) and (8, 4).
Find the slope using the slope formula: m = %28y2-y1%29%2F%28x2-x1%29
Assign these as follows
x1=2; y1=-1
x2=8; y2=4
:
m = %284-%28-1%29%29%2F%288-2%29 = %284%2B1%29%2F%288-2%29 = 5%2F6 is the slope
:
a. Write an equation for the line in point-slope form.
The point-slope form: y - y1 = m(x - x1)
y - (-1) = 5%2F6(x - 2)
y + 1 = 5%2F6x - 5%2F6*2
y + 1 = 5%2F6x - 5%2F3
y = 5%2F6x - 5%2F3 -1
y = 5%2F6x - 5%2F3 - 3%2F3
:
y = 5%2F6x - 8%2F3; is the point-slope form
:
;
b. Rewrite the equation in standard form using integers.
y = 5%2F6x - 8%2F3
Multiply each term by 6 to get rid of the denominators, results
6y = 5x - 2(8)
6y = 5x - 16
-5x + 6y = - 16
They prefer the 1s term to be positive, multiply by -1
5x - 6y = 16
;
:
You can check our equation:
substitute 8 for x and 4 for y and ensure they = 16