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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

User Him Hah
by
8.4k points

1 Answer

4 votes

Answer:


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}

User Michael Homer
by
7.7k points

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