Question

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

Answer 1

Answer:

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:

$y=\frac{1}{3}x+1\implies Slope,m=\frac{1}{3}$

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:

$\begin{gathered} m_1\times\frac{1}{3}=-1 \\ \implies Slope\text{ of line L}=-3 \end{gathered}$

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:

$y=-3x+5$