Question

A line passes through (2, (2, – 1) and (4, 5) . Which answer is the equation of the line? 0-3x + 5y = 13 6 -3x + y = 17 0-3x + 5y = -13 0-3x + y = -7

Answer 1

A line passes through

(2, -1) and (4, 5)

We can say, given:

`\begin{gathered} (x_1,y_1)=(2,-1) \\ \text{and} \\ (x_2,y_2)=(4,5) \end{gathered}`

The equation of a line is given as:

`y=mx+b`

Where

m is slope and b is y-intercept

Now, finding the slope using the slope formula:

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ m=(5+1)/(4-2) \\ m=(6)/(2) \\ m=3 \end{gathered}`

So, the equation becomes:

y = 3x + b

Putting a point in (x,y), such as (4,5), we have:

y = 3x + b

5 = 3(4) + b

5 = 12 + b

b = 5 - 12

b = -7

Thus,

equation of the line >>> y = 3x - 7

Re-arranging in standard form >>> -3x + y = -7

Last Answer choice is right.