Answer:
[tex]\displaystyle y=-\frac{1}{5}x+\frac{17}{5}[/tex]
Step-by-step explanation:
Equation of a line
A line can be represented by an equation of the form
[tex]y=mx+b[/tex]
Where x is the independent variable, m is the slope of the line, b is the y-intercept and y is the dependent variable.
We need to find the equation of the line passing through the point (7,2) and is perpendicular to the line y=5x-2.
Two lines with slopes m1 and m2 are perpendicular if:
[tex]m_1.m_2=-1[/tex]
The given line has a slope m1=5, thus the slope of our required line is:
[tex]\displaystyle m_2=-\frac{1}{m_1}=-\frac{1}{5}[/tex]
The equation of the line now can be expressed as:
[tex]\displaystyle y=-\frac{1}{5}x+b[/tex]
We need to find the value of b, which can be done by using the point (7,2):
[tex]\displaystyle 2=-\frac{1}{5}*7+b[/tex]
Operating:
[tex]\displaystyle 2=-\frac{7}{5}+b[/tex]
Multiplying by 5:
[tex]10=-7+5b[/tex]
Operating:
[tex]10+7=5b[/tex]
Solving for b:
[tex]\displaystyle b=\frac{17}{5}[/tex]
The equation of the line is:
[tex]\boxed{\displaystyle y=-\frac{1}{5}x+\frac{17}{5}}[/tex]
