Question

HELP ME HELP ME please !!! 10 points

Answer 1

The slope is
`(3)/(2)`

The y-intercept is 9

Explanation:

The form of the equation that passes through two points (x1, y1) and (x2, y2) is y = m x + b, where

• m is the slope of the line whose rule is
  `m=(y2-y1)/(x2-x1)`

• b is the y-intercept, you can find it by substituting x, y in the equation by (x1, y1) OR (x2, y2)

Let us solve the question:

Choose any two-point from the table

∵ The line passes through the points (2, 12) and (4, 15)

∴ x1 = 2 and x2 = 4

∴ y1 = 12 and y2 = 15

→ Use the rule of m to find it

∵
`m=(15-12)/(4-2)=(3)/(2)`

∴ m =
`(3)/(2)`

∴ The slope is
`(3)/(2)`

→ Substitute its value in the form of the equation above

∴ y =
`(3)/(2)` x + b

→ To find b substitute x and y by x1 and y1

∴ 12 =
`(3)/(2)` (2) + b

∴ 12 = 3 + b

→ Subtract 3 from both sides

∴ 12 -3 = 3 - 3 + b

∴ 9 = b

∴ The y-intercept is 9