STEP - BY - STEP EXPLANATION
What to find?
Equation of a line.
Given:
Perpendicular equation; y=-1/5 x - 3
Point(1,2)
Step 1
Find the slope of the perpendicular line.
Comparing the line with y=mx + c
[tex]slope(m)=-\frac{1}{5}[/tex]
Step 2
Determine thee slope of the new equation.
Slope of perpendicular lines have the following characteristic;
[tex]m_1m_2=-1[/tex]
where m2 is the slope of the new equation.
[tex]\begin{gathered} -\frac{1}{5}m_2=-1 \\ \\ m_2=-1\times-\frac{5}{1} \\ \\ =5 \end{gathered}[/tex]
Step 3
Find the intercept(c) using the formula below:
[tex]y=mx+c[/tex]
Substitute x=1 y=2 and m=5
[tex]\begin{gathered} 2=5(1)+c \\ \\ c=2-5 \\ \\ =-3 \end{gathered}[/tex]
Step 4
Form the equation of the line by substituting m=5 and c=-3 into the general equation.
[tex]y=5x+(-3)[/tex]
ANSWER
y= 5x + (-3)
