Answer:
Step-by-step explanation:
The equation of a straight line can be represented in the slope-intercept form, y = mx + c
Where c = intercept
For two lines to be perpendicular, the slope of one line is the negative reciprocal of the other line. The equation of the given line is
(5x-5y)/4= (4x-4)/2
Cross multiplying
2(5x - 5y) = 4(4x - 4)
10x - 10y = 16x - 16
10y = - 6x + 16
y = -6x/10 + 16/10
Comparing with the slope intercept form,
Slope, m = - 6/10
This means that the slope of the line that is perpendicular to it is 10/6
The given points are (10,7)
To determine c,
We will substitute m = 10/6, y = 7 and x = 10 into the equation, y = mx + c. It becomes
7 = 10/6 × 10 + c
7 = 100/6 + c
7 = 50/3 + c
c = 7 - 50/3
c = - 29/3
The equation becomes
y = 10x/6 - 29/3
