SOLUTION: 1.find the slope and intercept of -4x+5y=25. 2.Find the slope of any line parallel to the line through points (12,5) and (10,4).

Algebra ->  Linear-equations -> SOLUTION: 1.find the slope and intercept of -4x+5y=25. 2.Find the slope of any line parallel to the line through points (12,5) and (10,4).      Log On


   

Question 120575: 1.find the slope and intercept of -4x+5y=25.
2.Find the slope of any line parallel to the line through points (12,5) and (10,4).
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
#1
Solved by pluggable solver: Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa)
Convert from standard form (Ax+By = C) to slope-intercept form (y = mx+b)


-4x%2B5y=25 Start with the given equation


-4x%2B5y%2B4x=25%2B4x Add 4x to both sides


5y=4x%2B25 Simplify


%285y%29%2F%285%29=%284x%2B25%29%2F%285%29 Divide both sides by 5 to isolate y


y+=+%284x%29%2F%285%29%2B%2825%29%2F%285%29 Break up the fraction on the right hand side


y+=+%284%2F5%29x%2B5 Reduce and simplify


The original equation -4x%2B5y=25 (standard form) is equivalent to y+=+%284%2F5%29x%2B5 (slope-intercept form)


The equation y+=+%284%2F5%29x%2B5 is in the form y=mx%2Bb where m=4%2F5 is the slope and b=5 is the y intercept.





#2
Solved by pluggable solver: Finding the slope


Slope of the line through the points (12, 5) and (10, 4)



m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29


m+=+%284+-+5%29%2F%2810+-+12%29


m+=+%28-1%29%2F%28-2%29


m+=+1%2F2



Answer: Slope is m+=+1%2F2





Remember, parallel lines have equal slopes. So any line parallel to the line through points (12,5) and (10,4) also has the slope m=1%2F2