Question

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

Answer 1

Answer:

C

Step-by-step 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:

$\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$

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:

$\displaystyle m=\frac{6-2}{4-0}$

Evaluate:

$\displaystyle m=\frac{4}{4}=1$

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.