SOLUTION: 1) how do u write an equation in slope-intercept form of the line that passes through (2,-7) and is parallel to the graph of y=x-2? 2) (2,3), y=x+5 3) (-5,-4), 2x+3

Question 119809:
1) how do u write an equation in slope-intercept form of the line that passes through (2,-7) and is parallel to the graph of y=x-2?

2) (2,3), y=x+5

3) (-5,-4), 2x+3y=-1
Found 2 solutions by jim_thompson5910, checkley71:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
#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,-7), 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

Combine like terms

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 (,)

#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 (2,3), 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

Add to both sides to isolate y

Combine like terms

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 (,)

#3

First convert the standard equation into slope intercept form

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)

Start with the given equation

Subtract 2x from both sides

Simplify

Divide both sides by 3 to isolate y

Break up the fraction on the right hand side

Reduce and simplify

The original equation (standard form) is equivalent to (slope-intercept form)

The equation is in the form where is the slope and is the y intercept.

Now let's find the equation of the line that is parallel to which goes through (-5,-4)

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 (-5,-4), 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 (,)

Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
Y=mX+b HERE WE HAVE A SLOPE OF 1 & X,Y VALUES OF (2,-7) SO WE USE THESE VALUES IN THE LINE EQUATION & SOLVE FOR b THE Y INTYERCEPT.
1) -7=1*2+b
-7=2+b
b=-7-2
b=-9
SO THE LINE EQUATION IS:
Y=X-9
-----------------------------------
2) Y=X+5 (2,3)
3=2*1+b
3=2+b
b=3-2
b=1
SO THE LINE EQUATION IS:
Y=X+1
-----------------------------------------
3) 2X+3Y=-1 (-5,-4)
3Y=-2X-1
Y=-2X/3-1/3
-4=-2/3*-5+b
-4=10/3+b
b=-4-10/3
b=(-12-10)/3
b=-22/3
SO THE LINE EQUATION IS:
Y=-2X/3-22/3

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