Question

Find the value of R so the line passes through each point (3,5) (-3,r) m=3/4

Answer 1

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Answer 2

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.