SOLUTION: Hi I have two problems I need help with. Thanks Find an equation of the line containing the given pair of points. Write answer in slope intercept form. 1.(-5,8) and (6,-4)

Algebra ->  Graphs -> SOLUTION: Hi I have two problems I need help with. Thanks Find an equation of the line containing the given pair of points. Write answer in slope intercept form. 1.(-5,8) and (6,-4)       Log On


   

Question 243724: Hi I have two problems I need help with. Thanks
Find an equation of the line containing the given pair of points. Write answer in slope intercept form.
1.(-5,8) and (6,-4)
Solve using either elimination or substitution. If the system has either no solution or an infinite number of solutions, state this.
2.y=6x+41
4x+9y=-95
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1



First let's find the slope of the line through the points and


Note: is the first point . So this means that x%5B1%5D=-5 and y%5B1%5D=8.
Also, is the second point . So this means that x%5B2%5D=6 and y%5B2%5D=-4.


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%28-4-8%29%2F%286--5%29 Plug in y%5B2%5D=-4, y%5B1%5D=8, x%5B2%5D=6, and x%5B1%5D=-5


m=%28-12%29%2F%286--5%29 Subtract 8 from -4 to get -12


m=%28-12%29%2F%2811%29 Subtract -5 from 6 to get 11


So the slope of the line that goes through the points and is m=-12%2F11


Now let's use the point slope formula:


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y-8=%28-12%2F11%29%28x--5%29 Plug in m=-12%2F11, x%5B1%5D=-5, and y%5B1%5D=8


y-8=%28-12%2F11%29%28x%2B5%29 Rewrite x--5 as x%2B5


y-8=%28-12%2F11%29x%2B%28-12%2F11%29%285%29 Distribute


y-8=%28-12%2F11%29x-60%2F11 Multiply


y=%28-12%2F11%29x-60%2F11%2B8 Add 8 to both sides.


y=%28-12%2F11%29x%2B28%2F11 Combine like terms.


So the equation that goes through the points and is y=%28-12%2F11%29x%2B28%2F11




# 2

4x%2B9y=-95


4x%2B9%286x%2B41%29=-95 Plug in y=6x%2B41


4x%2B54x%2B369=-95 Distribute.


58x%2B369=-95 Combine like terms on the left side.


58x=-95-369 Subtract 369 from both sides.


58x=-464 Combine like terms on the right side.


x=%28-464%29%2F%2858%29 Divide both sides by 58 to isolate x.


x=-8 Reduce.


y=6x%2B41 Go back to the first equation.


y=6%28-8%29%2B41 Plug in x=-8


y=-48%2B41 Multiply


y=-7 Add


So the solutions are x=-8 and y=-7 which form the ordered pair (-8,-7)