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

Solution:

The solution given in the question is given below as

$y=\frac{1}{2}x-2$

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,

$m_1=\frac{1}{2}$

Note:

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

$m_1=m_2$

Therefore,

$m_2=\frac{1}{2}$

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

$m_2=\frac{y-y_1}{x-x_1}$

By substituting the values, we will have

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

Hence,

The final answer is

$y=\frac{1}{2}x+7$