Question

Complete the slope-intercept form of an equation that represents the relationship in the table.

x
x
y
y
1
1
−1
-
1
4
4
8
8

Answer 1

y = 3x - 4

Explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (1, - 1) and (x₂, y₂ ) = (4, 8) ← 2 ordered pairs from the table

m =
`(8-(-1))/(4-1)` =
`(8+1)/(3)` =
`(9)/(3)` = 3 , then

y = 3x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, 8 )

8 = 12 + c ⇒ c = 8 - 12 = - 4

y = 3x - 4 ← equation representing the table

Answer 2

`\bf \implies{y = 3x - 4}`

Explanation:

To Find :- slope intercept form

Solution :- Given

when x = 1 => y = -1 ...(1)

& x = 4 => y = 8 ...(2)

Let slope intercept form is

y = mx + c ...(3)

by (1) & (3) at (1,-1)

-1 = m + c ...(4)

by (2) & (3) at (4,8)

8 = 4m + c ... (5)

eq. (5) - (4)

9 = 3m => m = 3

by (4) c = -1 - m = -1 - 3 = -4

Hence,

• y = 3x - 4