Question

Which of the following is the equation of the line that passes through the point (2, -1)and has a slope of?A 3x - 4y = 10B 4x - 3y = 10C 3x - y = 4D 3x - 4y = 4

Answer 1

The equation of a line is given as:

y = mx + c

where the slope is m and c is the constant of proportionality.

The coordinates of a point on the line has been given to us as (2, -1) i.e. x = 2 and y = -1.

The only thing unknown to write the equation of the line is the constant C.

Therefore, in order to get C, we should substitute the values of x, y and m into the equation of the line:

y = mx+ C

`\begin{gathered} y=mx+c \\ y=-1,x=2,m=(3)/(4) \\ -1=(3)/(4)*2+c \\ -1=(3)/(2)+c \\ \text{subtract }(3)/(2)\text{ from both sides} \\ -1-(3)/(2)=c \\ c=-(5)/(2) \end{gathered}`

Now that we have the value of c, we can proceed to write the equation as:

`\begin{gathered} y=(3)/(4)x+-(5)/(2) \\ y=(3)/(4)x-(5)/(2) \\ \\ \text{Multiply both sides by 4} \\ 4* y=4*((3)/(4)x-(5)/(2)) \\ 4y=4*(3)/(4)x-4*(5)/(2) \\ 4y=3x-10 \\ rearrange\text{ the equation} \\ 3x-4y=10 \end{gathered}`

Therefore the final answer is: 3x - 4y = 10 (A)