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

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) (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
an equation of the line is , where is a slope and is y-intercept
you are given:
the line that passes through the origin, which means the line that passes through the point (,)
the line that passes through the origin, which means
go to , substitute what is given
...solve for

so, your line is:

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 ; it must be
in this case is y coordinate of given point;
so, your equation is:

3. Write an equation of the line containing (2,-1) and parallel to the graph of .
given:
(2,-1)
=>=>

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 (its from the slope of which is also ). 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:

where m is the slope and (,) is the given point

Plug in , , and

Distribute

Multiply

Subtract from both sides to isolate y

Make into equivalent fractions with equal denominators

Combine the fractions

Reduce any fractions

So the equation of the line that is parallel to and goes through (,) is

So here are the graphs of the equations and

graph of the given equation (red) and graph of the line (green) that is parallel to the given graph and goes through (,)

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