SOLUTION: 1.Find an equation of the line that passes through the origin and has a slope of - 5 2. Write an equation in standard form of the line satisfying the following condition. The l

Algebra ->  Graphs -> SOLUTION: 1.Find an equation of the line that passes through the origin and has a slope of - 5 2. Write an equation in standard form of the line satisfying the following condition. The l      Log On


   

Question 1122738: 1.Find an equation of the line that passes through the origin and has a slope of - 5
2. Write an equation in standard form of the line satisfying the following condition.
The line goes through ​(3​,2​), and is horizontal.
3. Write an equation of the line containing ​(2​,-1​) and parallel to the graph of 7x-5y=4.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
1.Find an equation of the line that passes through the origin and has a slope of -+5
an equation of the line is y=mx%2Bb, where m is a slope and b is y-intercept
you are given:
the line that passes through the origin, which means the line that passes through the point (0,0)
the line that passes through the origin, which means m=-5
go to y=mx%2Bb, substitute what is given
0=-5%2A0%2Bb...solve for b
b=0
so, your line is: y=+-5x


2. Write an equation in standard form of the line satisfying the following condition.
The line goes through ​(3​,2​), and is horizontal.
if given that the line is horizontal, we know that horizontal line has a slope equal ti zero; it must be y=b
in this case b is y coordinate of given point; b=2
so, your equation is: y=2



3. Write an equation of the line containing ​(2​,-1​) and parallel to the graph of 7x-5y=4.
given:
​(2​,-1​)
7x-5y=4=>7x-4=5y=>y=%287%2F5%29x-4%2F5

Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line


Since any two parallel lines have the same slope we know the slope of the unknown line is 7%2F5 (its from the slope of y=%287%2F5%29%2Ax%2B4%2F5 which is also 7%2F5). Also since the unknown line goes through (2,-1), we can find the equation by plugging in this info into the point-slope formula

Point-Slope Formula:

y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope and (x%5B1%5D,y%5B1%5D) is the given point



y%2B1=%287%2F5%29%2A%28x-2%29 Plug in m=7%2F5, x%5B1%5D=2, and y%5B1%5D=-1



y%2B1=%287%2F5%29%2Ax-%287%2F5%29%282%29 Distribute 7%2F5



y%2B1=%287%2F5%29%2Ax-14%2F5 Multiply



y=%287%2F5%29%2Ax-14%2F5-1Subtract -1 from both sides to isolate y

y=%287%2F5%29%2Ax-14%2F5-5%2F5 Make into equivalent fractions with equal denominators



y=%287%2F5%29%2Ax-19%2F5 Combine the fractions



y=%287%2F5%29%2Ax-19%2F5 Reduce any fractions

So the equation of the line that is parallel to y=%287%2F5%29%2Ax%2B4%2F5 and goes through (2,-1) is y=%287%2F5%29%2Ax-19%2F5


So here are the graphs of the equations y=%287%2F5%29%2Ax%2B4%2F5 and y=%287%2F5%29%2Ax-19%2F5



graph of the given equation y=%287%2F5%29%2Ax%2B4%2F5 (red) and graph of the line y=%287%2F5%29%2Ax-19%2F5(green) that is parallel to the given graph and goes through (2,-1)