Question

Can you help me to understand this question and answer it.find the equation of a line that passes through the point (-4, 5) and is parallel to the given equation. y=1/2x -2

Answer 1

The solution given in the question is given below as

`y=(1)/(2)x-2`

The coordinates given in the question are

`(x_1,y_1)=(-4,5)`

Concept:

The general formula of an equation of a line in slope-intercept form is given below as

`\begin{gathered} y=mx+c \\ \text{where,} \\ m=\text{slope} \\ c=y-\text{intercept} \end{gathered}`

By comparing coeficient,

`m_1=(1)/(2)`

Note:

Two lines are said to be parallel if they have the same slope

`m_1=m_2`

Therefore,

`m_2=(1)/(2)`

The formula used to calculate the equation of a line is given below as

`m_2=(y-y_1)/(x-x_1)`

By substituting the values, we will have

`\begin{gathered} m_2=(y-y_1)/(x-x_1) \\ (1)/(2)=(y-5)/(x-(-4)) \\ (1)/(2)=(y-5)/(x+4) \\ \text{cross mutilply, we will have} \\ 2(y-5)=1(x+4) \\ 2y-10=x+4 \\ 2y=x+4+10 \\ 2y=x+14 \\ \text{divide all through by 2} \\ (2y)/(2)=(x)/(2)+(14)/(2) \\ y=(1)/(2)x+7 \end{gathered}`

Hence,

The final answer is

`y=(1)/(2)x+7`