The answer is
[tex]y = - \frac{1}{5} x + \frac{24}{5} [/tex]
Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
y - 5x = 1
y = 5x + 1
Comparing with the above formula
The slope / m of the line is 5
Since the is perpendicular to y = 5x + 1 it's slope it's the negative inverse of y = 5x + 1
That's
Slope of the perpendicular line = - 1/5
Equation of the line using point (-1,5) is
[tex]y - 5 = - \frac{1}{5} (x + 1)[/tex]
[tex]y - 5 = - \frac{1}{5} x - \frac{1}{5} [/tex]
[tex]y = - \frac{1}{5} x - \frac{1}{5} + 5[/tex]
We have the final answer as
[tex]y = - \frac{1}{5} x + \frac{24}{5} [/tex]
Hope this helps you
Answer:
[tex]\huge\boxed{y=-\dfrac{1}{5}x+\dfrac{24}{5}\to x+5y=24}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
Let
[tex]k:y=m_1x+b_1;\ l:y=m_2x+b_2[/tex]
therefore
[tex]k||l\iff m_1=m_2\\k\perp l\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}[/tex]
We have the equation of a line in the standard form. Convert it to the slope-intercept form:
[tex]y-5x=1[/tex] add 5x to both sides
[tex]y-5x+5x=1+5x\\\\y=5x+1\to m_1=5;\ b_1=1[/tex]
Calculate the slope:
[tex]m_2=-\dfrac{1}{5}[/tex]
Substitute the value of a slope and the coordinates of the given point (-1, 5) to the equation of a line:
[tex]y=m_2x+b[/tex]
[tex]5=\left(-\dfrac{1}{5}\right)(-1)+b[/tex]
[tex]5=\dfrac{1}{5}+b[/tex] subtract 1/5 from both sides
[tex]5-\dfrac{1}{5}=\dfrac{1}{5}-\dfrac{1}{5}+b[/tex]
[tex]\dfrac{25}{5}-\dfrac{1}{5}=b\\\\\dfrac{24}{5}=b\to b=\dfrac{24}{5}[/tex]
Final answer:
[tex]y=-\dfrac{1}{5}x+\dfrac{24}{5}[/tex]
convert to the standard form (Ax + By = C):
[tex]y=-\dfrac{1}{5}x+\dfrac{24}{5}[/tex] multiply both sides by 5
[tex]5y=(5)\left(-\dfrac{1}{5}x\right)+(5)\left(\dfrac{24}{5}\right)[/tex]
[tex]5y=-x+24[/tex] add x to both sides
[tex]x+5y=24[/tex]
