Respuesta :
Answer:
y = - [tex]\frac{5}{4}[/tex] x - [tex]\frac{13}{4}[/tex]
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
y + 6 = [tex]\frac{4}{5}[/tex](x - 5) ← is in point- slope form
with slope m = [tex]\frac{4}{5}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{4}{5} }[/tex] = - [tex]\frac{5}{4}[/tex]
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = - [tex]\frac{5}{4}[/tex] , thus
y = - [tex]\frac{5}{4}[/tex] x + c ← is the partial equation
To find c substitute (- 1, - 2) into the partial equation
- 2 = [tex]\frac{5}{4}[/tex] + c ⇒ c = - 2 - [tex]\frac{5}{4}[/tex] = - [tex]\frac{13}{4}[/tex]
y = - [tex]\frac{5}{4}[/tex] x - [tex]\frac{13}{4}[/tex] ← equation of perpendicular line
Step-by-step explanation:
Hey there!
Given,
The line is passing through point (-1,-2) and perpendicular to the line (y+6) = 4/5(x-5).
Now,
The equation of a st.line passing through point (-1,-2) is,
[tex](y - y1) = m1(x - x1)[/tex]
Put all values.
[tex](y + 2) = m1(x + 1)[/tex]
It is the 1st equation.
Another equation is (y+6)= 4/5(x-5).
[tex]y = \frac{4}{5} x - 10[/tex]
From equation (ii) {After comparing the equation with y =mx+c}.
We get,
M2= 4/5.
Now,
As per the condition of perpendicular lines,
m1×m2= -1.
[tex]m1 \times \frac{4}{5} = - 1[/tex]
Simplify them to get answer.
[tex]4m1 = - 5[/tex]
Therefore the slope is, -5/4.
Now, keep the slope in 1st equation.
[tex](y + 2) = \frac{ - 5}{4} (x + 1)[/tex]
Simplify them to get answer.
[tex](y + 2) = \frac{ - 5}{4} x - \frac{5}{4} [/tex]
[tex]y = \frac{ - 5}{4} x - \frac{5}{4} - 2 [/tex]
[tex]y = \frac{ - 5}{4} x - \frac{13}{4} [/tex]
Therefore the required equation is y = -5/4x -13/2.
Hopeit helps....
