Answer:
[tex]y=-\frac{5}{2}x+17[/tex]
Step-by-step explanation:
Equation of the Line
The general equation of a line of slope m and y-intercept b can be expressed as:
[tex]y=mx+b[/tex]
The given equation is:
[tex]\displaystyle y=\frac{2}{5}x-7[/tex]
Its slope is m1=2/5. The required line is perpendicular to the other and let's assume its slope is m2. Two lines are perpendicular if their slopes comply with the relationship:
[tex]m_1m_2=-1[/tex]
The second slope can be calculated as:
[tex]\displaystyle m_2=-\frac{1}{m_1}[/tex]
[tex]\displaystyle m_2=-\frac{1}{2/5}=-\frac{5}{2}[/tex]
The equation of the required line is:
[tex]y=-\frac{5}{2}x+b[/tex]
To find the value of b, we use the point (8,-3):
[tex]-3=-\frac{5}{2}(8)+b[/tex]
[tex]-3=-20+b[/tex]
Solving for b:
b=17
The equation of the line is
[tex]\boxed{y=-\frac{5}{2}x+17}[/tex]
