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What ordered pair is a solution to this equation?

𝑦 = −𝑥 + 10

 

 

 

A line passes through (1,6) and (4,4)

 

What is the slope of the line?

 

 

Point (2,10); Slope 4.  Write an equation for the line? 

Guest Oct 4, 2017

Best Answer 

 #1
avatar+7336 
+2

To find an ordered pair, pick any number you want, plug it into the equation for  x  or  y , and solve for the other variable. I pick  0  for  x.

 

  y   =   -x + 10   =   -0 + 10   =   10

 

When  x = 0 ,  y = 10  . So an ordered pair is  (0, 10) .

 

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slope  =  \(\frac{\text{change in y}}{\text{change in x}}\,=\,\frac{y_2-y_1}{x_2-x_1}\,=\,\frac{4-6}{4-1}\,=\,-\frac{2}{3}\)

 

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The point slope form of the line is:

 

y - 10  =  4(x - 2)      This equation is correct as it is, but do you need it in slope-intercept form?

hectictar  Oct 4, 2017
 #1
avatar+7336 
+2
Best Answer

To find an ordered pair, pick any number you want, plug it into the equation for  x  or  y , and solve for the other variable. I pick  0  for  x.

 

  y   =   -x + 10   =   -0 + 10   =   10

 

When  x = 0 ,  y = 10  . So an ordered pair is  (0, 10) .

 

----------

 

slope  =  \(\frac{\text{change in y}}{\text{change in x}}\,=\,\frac{y_2-y_1}{x_2-x_1}\,=\,\frac{4-6}{4-1}\,=\,-\frac{2}{3}\)

 

----------

 

The point slope form of the line is:

 

y - 10  =  4(x - 2)      This equation is correct as it is, but do you need it in slope-intercept form?

hectictar  Oct 4, 2017
 #2
avatar
0

Yes please.

Guest Oct 4, 2017
 #3
avatar+7336 
+1

Okay... smiley  We need to get   y - 10  =  4(x - 2)   into the form: y  =  mx + b  .

 

y - 10  =  4(x - 2)          Add  10  to both sides of the equation.

 

y  =  4(x - 2) + 10         Distribute  4  to each term in parenthesees.

 

y  =  4x - 8  + 10          Combine the  -8  and  10  to get  2 .

 

y  =  4x + 2

hectictar  Oct 4, 2017

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