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Find t such that (t, 5) lies on the line through (0, 3) and (-8, 0)

Logic  Aug 27, 2018

Best Answer 

 #2
avatar+7336 
+2

Let's find the equation of the line that passes through  (0, 3)  and  (-8, 0) .

 

slope  =  [0 - 3] / [-8 - 0]   =   -3 / -8   =   3 / 8

 

The y-intercept is the y value when  x  is  0 .

We know that the line goes through the point (0, 3) , so when  x  is  0 ,  y is  3 .

The y-intercept is  3 .

 

The equation of the line in slope-intercept form is...

 

y  =  (3/8)x + 3

 

We also know that the line passes through the point  (t, 5) .

So we know it makes a true equation when  x  is  t  and  y  is  5 .

So let's plug in  t  for  x  and  5  for  y , and solve for  t .

 

5  =  (3/8)t + 3

                              Subtract  3  from both sides of the equation.

2  =  (3/8)t

                              Multiply both sides by  8/3 .

2 * 8/3  =  t

 

16/3  =  t

 

t  =  16/3

 

Here's an edit of terte's graph with the line  y = (3/8)x + 3  and the point  (16/3, 5)  added:

https://www.desmos.com/calculator/9ok5ecrcb1     smiley

hectictar  Aug 28, 2018
 #1
avatar+3270 
+3

We can first graph it:https://www.desmos.com/calculator/zwhxypzkrb

tertre  Aug 27, 2018
 #2
avatar+7336 
+2
Best Answer

Let's find the equation of the line that passes through  (0, 3)  and  (-8, 0) .

 

slope  =  [0 - 3] / [-8 - 0]   =   -3 / -8   =   3 / 8

 

The y-intercept is the y value when  x  is  0 .

We know that the line goes through the point (0, 3) , so when  x  is  0 ,  y is  3 .

The y-intercept is  3 .

 

The equation of the line in slope-intercept form is...

 

y  =  (3/8)x + 3

 

We also know that the line passes through the point  (t, 5) .

So we know it makes a true equation when  x  is  t  and  y  is  5 .

So let's plug in  t  for  x  and  5  for  y , and solve for  t .

 

5  =  (3/8)t + 3

                              Subtract  3  from both sides of the equation.

2  =  (3/8)t

                              Multiply both sides by  8/3 .

2 * 8/3  =  t

 

16/3  =  t

 

t  =  16/3

 

Here's an edit of terte's graph with the line  y = (3/8)x + 3  and the point  (16/3, 5)  added:

https://www.desmos.com/calculator/9ok5ecrcb1     smiley

hectictar  Aug 28, 2018

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