Asked by Annetta Johnson
Find the value of R so the line passes through each point (3,5) (-3,r) m=3/4
Answers
Answered by
connect 6th grader
idk
Answered by
Bosnian
The equation of a line passing through two points ( x1, y1 ) and ( x2, y2 ) is:
y - y1 = [ ( y2 - y1 ) / ( x2 - x1 ) ] ( x - x1)
Since:
m = ( y2 - y1 ) / ( x2 - x1 ) is slope.
y - y1 = m ∙ ( x - x1)
In this case:
x1 = 3 , y1 = 5
x2 = - 3 , y2 = r
Slope:
m = 3 / 4
m = ( y2 - y1 ) / ( x2 - x1 )
3 / 4 = ( r - 5 ) / ( - 3 - 3 )
3 / 4 = ( r - 5 ) / - 6
Cross multiply.
3 ∙ ( - 6 ) = 4 ∙ ( r - 5 )
- 18 = 4 r - 20
Add 20 to both sides.
2 = 4 r
4 r = 2
r = 2 / 4 = 2 ∙ 1 / 2 ∙ 2
r = 1 / 2
Check result.
The equation of a line passing through two points ( x1, y1 ) and ( x2, y2 ) is:
y - y1 = m ∙ ( x - x1)
y - 5 = 3 / 4 ∙ ( x - 3 )
y - 5 = 3 / 4 x - 9 / 4
Add 5 to both sides.
y = 3 / 4 x - 9 / 4 + 5 = 3 / 4 x - 9 / 4 + 20 / 4
y = 3 / 4 x + 11 / 4
is equation of your line.
For x = x1 = 3
y = y1 = ( 3 / 4 ) ∙ x1 + 11 / 4
y1 = ( 3 / 4 ) ∙ 3 + 11 / 4 = 9 / 4 + 11 / 4 = 20 / 4
y1 = 5
x1 = 3 , y1 = 5 is coordinate of first point.
For x = x2 = - 3
y = y2 = ( 3 / 4 ) ∙ x2 + 11 / 4
y2 = ( 3 / 4 ) ∙ ( - 3 ) + 11 / 4 = - 9 / 4 + 11 / 4 = 2 / 4 = 1 / 2 = r
y2 = r
x2 = - 3 , y2 = r is coordinate of second point.
y - y1 = [ ( y2 - y1 ) / ( x2 - x1 ) ] ( x - x1)
Since:
m = ( y2 - y1 ) / ( x2 - x1 ) is slope.
y - y1 = m ∙ ( x - x1)
In this case:
x1 = 3 , y1 = 5
x2 = - 3 , y2 = r
Slope:
m = 3 / 4
m = ( y2 - y1 ) / ( x2 - x1 )
3 / 4 = ( r - 5 ) / ( - 3 - 3 )
3 / 4 = ( r - 5 ) / - 6
Cross multiply.
3 ∙ ( - 6 ) = 4 ∙ ( r - 5 )
- 18 = 4 r - 20
Add 20 to both sides.
2 = 4 r
4 r = 2
r = 2 / 4 = 2 ∙ 1 / 2 ∙ 2
r = 1 / 2
Check result.
The equation of a line passing through two points ( x1, y1 ) and ( x2, y2 ) is:
y - y1 = m ∙ ( x - x1)
y - 5 = 3 / 4 ∙ ( x - 3 )
y - 5 = 3 / 4 x - 9 / 4
Add 5 to both sides.
y = 3 / 4 x - 9 / 4 + 5 = 3 / 4 x - 9 / 4 + 20 / 4
y = 3 / 4 x + 11 / 4
is equation of your line.
For x = x1 = 3
y = y1 = ( 3 / 4 ) ∙ x1 + 11 / 4
y1 = ( 3 / 4 ) ∙ 3 + 11 / 4 = 9 / 4 + 11 / 4 = 20 / 4
y1 = 5
x1 = 3 , y1 = 5 is coordinate of first point.
For x = x2 = - 3
y = y2 = ( 3 / 4 ) ∙ x2 + 11 / 4
y2 = ( 3 / 4 ) ∙ ( - 3 ) + 11 / 4 = - 9 / 4 + 11 / 4 = 2 / 4 = 1 / 2 = r
y2 = r
x2 = - 3 , y2 = r is coordinate of second point.
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