Question

Need help for question 8 and 9. I need the equation that’s passes through the points!

Answer 1

Explanation:

Question 8

Let the equation of a line passing through two points
`(x_1,y_1)` and
`(x_2,y_2)` is given by,

y = mx + b

Here, m = slope and y-intercept = b

Since, m =
`(y_2-y_1)/(x_2-x_1)`

For two points (1, 4) and (5, 8),

m =
`(8-4)/(5-1)`

m = 1

Equation will be,

y = (1)x + b

y = x + b

Since, this line passes through (1, 4),

4 = 1 + b

b = 3

Therefore, equation of the line will be,

y = x + 3

Question 9

Let the equation is y = mx + b

m =
`(y_2-y_1)/(x_2-x_1)`

For two points (2, 10) and (6, 4)

m =
`(10-4)/(2-6)`

m =
`-(3)/(2)`

By substituting the value of 'm' in the equation,

y =
`-(3)/(2)x+b`

Since, this line passes through (2, 10)

10 =
`-(3)/(2)(2)+b`

b = 10 + 2

b = 12

Therefore, equation of the line will be,

`y=-(3)/(2)x+12`