Question

create 2 liner equations in the form y=mx+bthe lines are perpendicular to eachother both lines pass through the point (3,-5)

Answer 1

The linear equations are to be written in the form:

$y=mx+b$

Let the lines be:

$\begin{gathered} \text{Line 1} \\ y=m_1x+b_1 \\ \text{Line 2} \\ y=m_2x+b_2 \end{gathered}$

Since both lines are perpendicular, we have that:

$m_1=-\frac{1}{m_2_{}}$

Therefore, the equation for Line 1 becomes:

$y=-\frac{x}{m_2}+b_1$

Assuming the slope m₂ is 2, we have the equations to be:

$\begin{gathered} \text{Line 1} \\ y=-\frac{x}{2}+b_1 \\ \text{Line 2} \\ y=2x+b_2 \end{gathered}$

We can get the values of b₁ and b₂ by substituting the values of x and y given to be the ordered pair (3, -5):

$\begin{gathered} \text{Line 1} \\ -5=-\frac{3}{2}+b_1 \\ b_1=-5+\frac{3}{2} \\ b_1=-3.5 \end{gathered}$

and

$\begin{gathered} \text{Line 2} \\ -5=2(3)+b_2 \\ b_2=-5-6 \\ b_2=-11 \end{gathered}$

Therefore, the 2 linear equations can be:

$\begin{gathered} y=-\frac{x}{2}-3.5\text{ ---------(1)} \\ y=2x-11\text{ ----------(2)} \end{gathered}$

The graph of the 2 equations are shown below: