Hi

1. What is the equation of a line that passes through points (-1, 2) and (5, 2) y = 2

7. What is the equation of a line with a point (-3, 0) and no slope? x = -3

 

  

2. What is the equation of a line with a slope of -2 and a y-intercept of 8?

  y = -2x + 8

3. What is the slope of a line parallel to the line whose equation is y - x = 5?

 y = x+ 5   parallel lines have equal slopes of m = 1

4. What is the equation of the line that passes through the point (1, 1) and has a y-intercept of 2.  

y = mx + 2  

1 = m + 2    m = -1

y = -x + 2

5. The slope of a line is 1/3 . What is the slope of a line perpendicular to this line? 

⊥ Lines have slopes that are negative reciprocals of one another:  m = - 3/1

6. What is the slope of a line perpendicular to the line whose equation is y = 2x + 5?  m =  -1/2

8. What is the equation of a line that passes through point (1, -2) and has a slope of 1/3 . 

y = (1/3)x + b

-2 = 1/3 + b

 -7/3 = b

y = (1/3)x -7/3

 

Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!
 1.





 
Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (,) and (,)

  

  

   Start with the slope formula (note: (,) is the first point (,) and  (,) is the second point (,))

  

  

   Plug in ,,,  (these are the coordinates of given points)

  

  

   Subtract the terms in the numerator  to get .  Subtract the terms in the denominator  to get 

  

    

  

  

   Reduce

  

    

  

  So the slope is

  

  

  

  

  

  

  

  ------------------------------------------------

  

  

Now let's use the point-slope formula to find the equation of the line:

  

  

  

  

  ------Point-Slope Formula------

   where  is the slope, and (,) is one of the given points

  

  

  So lets use the Point-Slope Formula to find the equation of the line

  

  

   Plug in , , and  (these values are given)

  

  

  

   Rewrite  as 

  

  

  

   Distribute 

  

  

   Multiply  and  to get . Now reduce  to get 


  

   Add  to  both sides to isolate y

  

  

   Combine like terms  and  to get  

  

  ------------------------------------------------------------------------------------------------------------

  

  Answer:

  

  

  

  So the equation of the line which goes through the points (,) and (,)  is:

  

  

  The equation is now in  form (which is slope-intercept form) where the slope is  and the y-intercept is 

  

  

  Notice if we graph the equation  and plot the points (,) and (,),  we get this: (note: if you need help with graphing, check out this solver)

  

  

   Graph of  through the points (,) and (,)

  

  

  Notice how the two points lie on the line. This graphically verifies our answer.

  

  

  







answer:  or in slope-intercept form 





2.





 
Solved by pluggable solver: FIND a line by slope and one point


  What we know about the line whose equation we are trying to find out:

    


      
it goes through point (0, 8)


      
it has a slope of -2


    


  

  First, let's draw a diagram of the coordinate system with point (0, 8) plotted with a little blue dot:

  

  

  

    Write this down: the formula for the equation, given point  and intercept a, is

  

     (see a paragraph below explaining why this formula is correct)

  

    Given that a=-2, and , we have the equation of the line:

  

    

  

    Explanation: Why did we use formula  ? Explanation goes here. We are trying to find equation y=ax+b. The value of slope (a) is already given to us. We need to find b. If a point (, ) lies on the line, it means that it satisfies the equation of the line. So, our equation holds for (, ):  Here, we know a, , and , and do not know b. It is easy to find out: . So, then, the equation of the line is: . 

  

    Here's the graph:

  

  

   







answer:  or in slope-intercept form 





3.



  or  







 
Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation  describes a sloping line. For any 

  equation ax+by+c = 0, slope is .
X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x =  c/a. 5/-1 = -5.
Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 5/1 = 5.
Slope is --1/1 = 1.
 Equation in slope-intercept form: y=1*x+5.







answer: slope is  





4.





 
Solved by pluggable solver: FIND EQUATION of straight line given 2 points
hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (1, 1) and (x2, y2) = (0, 2).

  Slope a is .

  Intercept is found from equation , or . From that, 

  intercept b is , or .

  

  y=(-1)x + (2)

  

  Your graph:

  

  

  







answer: or in slope-intercept form 







5.



if slope of the one line is , the slope of perpendicular line will be 





so, if , the slope of perpendicular line will be 





6.



equation  is already in slope-intercept form and you can see that slope is ; so, the slope of a line perpendicular to this line will be   





7.







 
Solved by pluggable solver: FIND a line by slope and one point


  What we know about the line whose equation we are trying to find out:

    


      
it goes through point (-3, 0)


      
it has a slope of 0


    


  

  First, let's draw a diagram of the coordinate system with point (-3, 0) plotted with a little blue dot:

  

  

  

    Write this down: the formula for the equation, given point  and intercept a, is

  

     (see a paragraph below explaining why this formula is correct)

  

    Given that a=0, and , we have the equation of the line:

  

    

  

    Explanation: Why did we use formula  ? Explanation goes here. We are trying to find equation y=ax+b. The value of slope (a) is already given to us. We need to find b. If a point (, ) lies on the line, it means that it satisfies the equation of the line. So, our equation holds for (, ):  Here, we know a, , and , and do not know b. It is easy to find out: . So, then, the equation of the line is: . 

  

    Here's the graph:

  

  

   







8.



the equation of a line that passes through point (1, -2) and has a slope of 1/3 







 
Solved by pluggable solver: FIND a line by slope and one point


  What we know about the line whose equation we are trying to find out:

    


      
it goes through point (1, -2)


      
it has a slope of 0.333333333333333


    


  

  First, let's draw a diagram of the coordinate system with point (1, -2) plotted with a little blue dot:

  

  

  

    Write this down: the formula for the equation, given point  and intercept a, is

  

     (see a paragraph below explaining why this formula is correct)

  

    Given that a=0.333333333333333, and , we have the equation of the line:

  

    

  

    Explanation: Why did we use formula  ? Explanation goes here. We are trying to find equation y=ax+b. The value of slope (a) is already given to us. We need to find b. If a point (, ) lies on the line, it means that it satisfies the equation of the line. So, our equation holds for (, ):  Here, we know a, , and , and do not know b. It is easy to find out: . So, then, the equation of the line is: . 

  

    Here's the graph:

  

  

   





you got:



...or in slope-intercept form 



...or in slope-intercept form  



or





...or in slope-intercept form  or



so the answer is : 



9.





 
Solved by pluggable solver: FIND a line by slope and one point


  What we know about the line whose equation we are trying to find out:

    


      
it goes through point (0, 3)


      
it has a slope of 1


    


  

  First, let's draw a diagram of the coordinate system with point (0, 3) plotted with a little blue dot:

  

  

  

    Write this down: the formula for the equation, given point  and intercept a, is

  

     (see a paragraph below explaining why this formula is correct)

  

    Given that a=1, and , we have the equation of the line:

  

    

  

    Explanation: Why did we use formula  ? Explanation goes here. We are trying to find equation y=ax+b. The value of slope (a) is already given to us. We need to find b. If a point (, ) lies on the line, it means that it satisfies the equation of the line. So, our equation holds for (, ):  Here, we know a, , and , and do not know b. It is easy to find out: . So, then, the equation of the line is: . 

  

    Here's the graph:

  

  

   







so the answer is : 









 

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