Question

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

Answer 1

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.