How to find equation of the lines

Hi. Can you please grade 5. Thanks.

1. Line passes through the point (5,1) and has a slope of 2 write an equation for this line

Solution:
y-1 = 2(x-5)
y-1 = 2x - 10
y = 2x -9

2. Find the equation for the line 1,-5 and -4,3

Solution:
Find gradient: (3-(-5)) / (-4-1) = -8/5

Equation: y -3 = -8/5 (x-(-4))
y-3 = -8/5 (x+4)
y-3 = (-8/5)x - (32/5)
y = (-8/5)x - (17/5)

3. Find the equation for the line -2,-1 and -3,4

Solution:
Find gradient: (4-(-1)) /(-3-(-2)) = -5

y-4 = -5(x-(-3))
y-4 = -5(x+3)
y-4 = -5x - 15
y=-5x - 11

4. Write equations for the horizontal and vertical lines passing through point (-1,9)

Solution:
Equation of horizontal line: y= 9

Equation of vertical line: x = -1

5. Consider the line -8x-2y=-5 what is the slope of the line perpendicular and parallel line

Solution:
2y = -8x + 5
y = -4x + (5/2)

Slope of the parallel line is: -4
Slope of the perpendicular line is: 1/4

Note that: If you multiply the slope of the parallel line and the slope of the perpendicular line, you must get -1

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