Answer:
1. Let the slope of the line passing through (4,7) be m.
Comparing y= 3x + 6 with y = nx +c, slope (n) = 3
Since the line passing through (4,7) is parallel to the line y=3x+6,
m = n
or, m = 3
The equation of line passing through (4,7) is given by:
y - 7 = 3 (x-4)
or, y - 7 = 3x - 12
or, 3x - y=5 is the required equation
2. Let the slope of the line passing through (-2,3) be m.
The slope of line y= -x + 4, n = -1
Since the line passing through (-2,3) and the line y= -x +4 are parallel to each other,
m = n
or, m = -1
The equation of the line passing through (-2,3) is given by:
y -3 =m (x +2)
or, y - 3 = -1 (x + 2)
or, -y+3 = x + 2
or, x +y = 1 is the required equation.
[Do 3 no. with same process]
4. Let the slope of the line passing through (-8,2) be m.
We have another line 5x - 4y = 4
or, 4y = 5x - 4
or, y = 5/4 x -1
Slope of the line y = 5/4 x -1, n = 5/4 = 1.25
[Notice, to compare any equation of the line with y = nx +c, the coefficient of y must be equal to 1. Here, the given line is 5x - 4y = 4 (Coefficient of y=4). The coefficient of the y was converted to 1.
You can continue doing 5 and 6 no. in same process. ]
The second and third pictures are not visible
