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:
[tex]\begin{equation} y=mx+b\text{ where }\begin{cases}m={slope} \\ b={y-intercept}\end{cases} \end{equation}[/tex]
Comparing the given line with the form above:
[tex]y=\frac{1}{3}x+1\implies Slope,m=\frac{1}{3}[/tex]
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:
[tex]\begin{gathered} m_1\times\frac{1}{3}=-1 \\ \implies Slope\text{ of line L}=-3 \end{gathered}[/tex]
The y-intercept of L is at (0,5), therefore:
[tex]y-intercept,b=5[/tex]
Substitute the slope, m=-3, and y-intercept, b=5 into the slope-intercept form.
[tex]\begin{gathered} y=mx+b \\ y=-3x+5 \end{gathered}[/tex]
The equation of line L is:
[tex]y=-3x+5[/tex]
