Question

What is the equation of the linear function in slope-intercept form described by this table?

What is the equation of the linear function in slope-intercept form described by this table?

x y
-2 5
-1 3
0 1
1 -1
2 -3
x y
-2 5
-1 3
0 1
1 -1
2 -3

Answer 1

`y=-2x+1`

Explanation:

The slope-intercept form of a linear function is:

→
`y = mx+b`

where
`m` is the line's slope and
`b` is it's y-intercept (the
`y`-value of the line when
`x=0`).

Remember that x is the horizontal distance from the origin (0, 0) and y is the vertical distance from the origin.

From the table, we can identify the y-intercept (
`b`) as:

• 
  `b = 1`

because when the line's
`x`-coordinate is 0, the
`y`-coordinate is 1.

Next, we can find the line's slope using the formula:

slope = rise / run

= Δy / Δx

where Δ means "change in" (i.e. Δx = "change in x").

We can plug in some values from the table to solve for slope. I will use the rows with (-2, 5) and (-1, 3):

slope = (3 - 5) / (-1 - (-2))

= -2 / (-1 + 2)

= -2 / 1

= -2

• 
  `m=-2`

Finally, we can plug these values into the slope-intercept form equation:

`y = mx+b`

`\boxed{y=-2x+1}`