Question

PLEASE HELP
L has y-intercept (0,5) and is perpendicular to the line with equation y=1/3x+1

Answer 1

y=-3x+5

Explanation:

Given a line L such that:

• L has y-intercept (0,5); and

,

• L is perpendicular to the line with equation y=(1/3)x+1.

We want to find the equation of the line in the slope-intercept form.

The slope-intercept form of the equation of a straight line is given as:

`\begin{equation} y=mx+b\text{ where }\begin{cases}m={slope} \\ b={y-intercept}\end{cases} \end{equation}`

Comparing the given line with the form above:

`y=(1)/(3)x+1\implies Slope,m=(1)/(3)`

Next, we find the slope of the perpendicular line L.

• Two lines are perpendicular if the product of their slopes is -1.

Let the slope of L = m1.

Since L and y=(1/3)x+1 are perpendicular, therefore:

`\begin{gathered} m_1*(1)/(3)=-1 \\ \implies Slope\text{ of line L}=-3 \end{gathered}`

The y-intercept of L is at (0,5), therefore:

`y-intercept,b=5`

Substitute the slope, m=-3, and y-intercept, b=5 into the slope-intercept form.

`\begin{gathered} y=mx+b \\ y=-3x+5 \end{gathered}`

The equation of line L is:

`y=-3x+5`