Answer:
The equation for line with point (2,-6) is given as : 5 x + 7 y = -32
Step-by-step explanation:
The given equation of line 1 is y= 7/5 x +6
Comparing it with the form y = mx + C, we get m = 7/5.
So, the slope of the equation 1 is ( 7/5).
Now, let us assume the slope of line 2, which is perpendicular to line 1 is p.
⇒ Slope of line 1 x Slope of line 2 = -1 (as lines are perpendicular)
⇒ p x ( 7/5) = -1
⇒ p = - (5/7)
Also, a point online 2 is given as ( 2,-6).
By POINT SLOPE FORMULA:
The line of the equation with point (x0,y0) and slope m is given as:
y - y0 = m (x -x0)
So, here the line equation (2) is given as
[tex]y - (-6) = \frac{-5}{7} (x -2)\\\implies 7(y +6) = -5(x-2)\\\implies 7y + 42 = - 5x + 10\\\implies 5x + 7y = -32[/tex]
Hence, the equation for line 2 with point (2,-6) is given as : 5x + 7y = -32
