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Line CD passes through points (0, 2) and (4, 6). Which equation represents line CD?

y = 2x – 2
y = 2x + 2
y = x + 2
y = x – 2

User EkcenierK
by
8.0k points

1 Answer

3 votes

Answer:

C

Explanation:

We know that line CD passes through the two points (0, 2) and (4, 6).

First and foremost, let’s find the slope of the line. We can use the slope formula:


\displaystyle m=(y_2-y_1)/(x_2-x_1)

Where (x₁, y₁) and (x₂, y₂) are our two points.

So, let’s let (0, 2) be (x₁, y₁) and (4, 6) be (x₂, y₂). Substitute appropriately:


\displaystyle m=(6-2)/(4-0)

Evaluate:


\displaystyle m=(4)/(4)=1

Hence, our slope is 1.

Now, we can use the slope-intercept form:


\displaystyle y=mx+b

Where m is our slope and b is our y-intercept.

Notice from our given points that we are given (0, 2).

So, our y-intercept is 2.

Therefore, we will substitute 1 for m and 2 for b. This yields:


\displaystyle y=(1)x+(2)

Simplify:


\displaystyle y=x+2

Hence, our answer is C.

User Ruslan Plastun
by
8.1k points

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