Question

Find the value of r so that the line that passes through the pair of points has the given slope. (2, r) , (4, 2) , m=5/2

Answer 1

(2, -3)

Explanation:

Write the equation of the line.

y = mx + b We need the slope and the y intercept. We have been give the slope (m) as 5/2. We will use that and the point (4,2) to figure out the y-intercept (b)

m = 5/2

y = 2 from the point given (4,2)

x = 4 from the point given (4,2) Another name for 4 is
`(4)/(1)`

y = mx + b substitute in what we know and solve for b

2 =
`(5)/(2)`
`((4)/(1))` + b

2 =
`(20)/(2)` + b

2 = 10 + b Subtract 10 from both sides

2 - 10 = 10 - 10 + b

-8 = b

Now that we have the slope (m) (5.2) and the y-intercept (b) -8. We can write the equation of the line.

y = mx + b

y =
`(5)/(2)` x - 8

We want to find out what is y when x = 2.

y =
`(5)/(2)`x = 8

y =
`(5)/(2)`(2) - 8

y = 5 - 8

y = -3