Answer:
Step-by-step explanation:
10) 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 given equation is
4x + 7y = 6
7y = - 4x + 6
y = -4x/7 + 6/7
Comparing with the slope intercept form,
Slope, m = -4/7
This means that the slope of the line that is perpendicular to it is 7/4
The given points are (-4,1)
To determine c,
We will substitute m = 7/4, y = 1 and x = - 4 into the equation, y = mx + c. It becomes
1 = 7/4 × -4 + c
1 = - 7 + c
c = 8
The equation becomes
y = 7x/4 + 8
11) 5x + 4y = 8 (10,5)
For two lines to be perpendicular, the slope of one line is the negative reciprocal of the other line. The given equation is
5x + 4y = 8
4y = - 5x + 8
y = -5x/4 + 2
Comparing with the slope intercept form,
Slope, m = -5/4
This means that the slope of the line that is perpendicular to it is 4/5
The given points are (10,5)
To determine c,
We will substitute m = 4/5, y = 5 and x = 10 into the equation, y = mx + c. It becomes
5 = 4/5 × 10 + c
5 = 8 + c
c = 5 - 8 = - 3
The equation becomes
y = 4x/5 - 3
12) 2x - 5y = - 10 (4 ,-5)
For two lines to be perpendicular, the slope of one line is the negative reciprocal of the other line. The given equation is
2x - 5y = -10
5y = 2x + 10
y = 2x/5 + 2
Comparing with the slope intercept form,
Slope, m = 2/5
This means that the slope of the line that is perpendicular to it is - 5/2
The given points are (4, -5)
To determine c,
We will substitute m = - 5/2, y = - 5 and x = 4 into the equation, y = mx + c. It becomes
- 5 = - 5/2 × 4 + c
- 5 = -10 + c
c = - 5 + 10 = 5
The equation becomes
y = - 5x/2 + 5
