Question

1. Line m passes through points (1, 2) and (-3, -4). What is the equation ofthe line parallel to line m that passes through point (0,5)?Ax + 5x + 5D.B.

Answer 1

Step 1

Given; Line m passes through points (1, 2) and (-3, -4). What is the equation of the line parallel to line m that passes through point (0,5)?

Step 2

We will find the slope of line m

`\begin{gathered} slope=(y_2-y_1)/(x_2-x_1) \\ slope=(-4-2)/(-3-1)=-(6)/(-4)=(3)/(2) \end{gathered}`

Step 3

What is the equation of the line parallel to line m that passes through point (0,5)?

Parallel lines have the same slope. Thus

`m_1=m_2=(3)/(2)`

The equation of a line in slope-intercept form is;

`\begin{gathered} y=mx+b \\ y=(3)/(2)x+b \\ b=y-intercept \\ y=5,x=0 \end{gathered}`

Thus, the y-intercept of the required line will be;

`\begin{gathered} 5=(3)/(2)(0)+b \\ b=5 \end{gathered}`

The answer will be;

`\begin{gathered} y=1.5x+5 \\ or \\ y=(3)/(2)x+5 \end{gathered}`