Which of the linear equations represents the graphed line?

A) y = 3
2
x + 1

B) y = 2
3
x + 1

C) y = -2
3
x + 1

D) y = -3
2
x + 1

Question

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jimthompson5910 jimthompson5910 · Answer 1 · 2018-11-07T23:24:41+01:00

Answer: [tex]y = \frac{2}{3}x + 1[/tex] (choice B)

The y intercept is 1 as this is where the graph crosses the y axis. So b = 1

The slope is m = 2/3 because we go up 2 for each time we move 3 units to the right. Example: moving from (0,1) to (3,3)

That means y = mx+b turns into [tex]y = \frac{2}{3}x+1[/tex]

This looks like choice B is the closest match though the formatting you posted is a bit jumbled.

vintechnology vintechnology · Answer 2 · 2021-11-03T12:23:02+01:00

The linear equation of the graph is y = 2/3 x + 1

Let's find the slope of the graph using the coordinates (0, 1) (-3, -1)

m = y₂ - y₁ / x₂ - x₁

m = -1 - 1 / -3 - 0

m = -2/-3

m = 2/3

Using the slope intercept form,

y = mx + c

where

m = slope

c = y- intercept(This is when x = 0)

Therefore,

c = 1

Finally, the equation will be

y = 2/3 x + 1

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