Question

Which line is parallel to the line given belowy = – 3х – 7=52 – 2 = 82x — 5y = 30ООООО 2х + 5 = - 5О 5х + 2y = 4

Answer 1

The general equation of a line is given as

`\begin{gathered} y=mx+c \\ \text{where} \\ m=\text{slope / gradient} \\ c=\text{intercept on the y axis} \end{gathered}`

Two lines are said to be parallel when they have the same slope or gradient that is

`\begin{gathered} m_1=m_2 \\ m_{1=\text{slope of the first line}} \\ m_{2=\text{slope of the second line}} \end{gathered}`

The equation of the line given is

`y=-(5)/(2)x-7`

By comparing coefficients,

`m_1=-(5)/(2)`

So from the options, we will figures out the equation that has the same gradient as -5/2

`\begin{gathered} 5x-2y=8 \\ -2y=-5x+8 \\ \text{divide all through bu -2} \\ -(2y)/(-2)=-(5x)/(-2)+(8)/(-2) \\ y=(5)/(2)x-4 \end{gathered}`

The slope above is 5/2 therefore the option A is not parallel to the line

`\begin{gathered} 2x-5y=30 \\ -5y=-2x+30 \\ -(5y)/(-5)=-(2x)/(-5)+(30)/(-5) \\ y=(2)/(5)x-6 \end{gathered}`

The slope above is 2/5 therefore Option B is not parallel to the line also

`\begin{gathered} 2x+5y=-5 \\ 5y=-2x-5 \\ (5y)/(5)=-(2x)/(5)-(5)/(5) \\ y=-(2)/(5)x-1 \end{gathered}`

The slope above is -2/5 Therefore Option C is also not parallel to the line

`\begin{gathered} 5x+2y=4 \\ 2y=-5x+4 \\ (2y)/(2)=-(5x)/(2)+(4)/(2) \\ y=-(5)/(2)x+2 \end{gathered}`

The slope above is -5/2 which is the same as the slope in the question

Therefore,

The correct answer is OPTION D