The equation of the each line in slope-intercept form are:
1. y = 3x + 11
2. y = -4x + 14
3. y = -1/3x + 8/3
4. y = 2x - 8
5. y = 5/2x - 6
6. y = 5x - 38
<h3>What is the Equation of Parallel Lines?</h3>
The equation of a line in slope-intercept form is, y = mx + b, where m is the slope, and if the lines are parallel, they will have the same value as m; b is the y-intercept.
However, for perpendicular lines, their slopes are negative reciprocal of each other.
1. Substitute m = 3 and (x, y) = (-3, 2) into y = mx + b:
2 = 3(-3) + b
2 = -9 + b
2 + 9 = b
11 = b
b = 11
Substitute m = 3 and b = 11 into y = mx + b:
y = 3x + 11 [slope-intercept form]
2. Substitute m = -4 and (x, y) = (4, -2) into y = mx + b:
-2 = -4(4) + b
-2 = -16 + b
b = 14
Substitute m = -4 and b = 14 into y = mx + b:
y = -4x + 14 [slope-intercept form]
3. Substitute m = -1/3 and (x, y) = (5, 1) into y = mx + b:
1 = -1/3(5) + b
1 = -5/3 + b
1 + 5/3 = b
b = 8/3
Substitute m = -1/3 and b = 8/3 into y = mx + b:
y = -1/3x + 8/3 [slope-intercept form]
4. The slope of y = 2x + 4 is 2
Substitute m = 2 and (x, y) = (3, -2) into y = mx + b:
-2 = 2(3) + b
-2 = 6 + b
-2 - 6 = b
-8 = b
b = -8
Substitute m = 2 and b = -8 into y = mx + b:
y = 2x - 8 [slope-intercept form]
5. 2y = 5x + 1 can be written in slope-intercept form as, y = 5/2x + 1/2
The slope of 2y = 6x + 1 is 5/2.
Substitute m = 5/2 and (x, y) = (2, -1) into y = mx + b:
-1 = 5/2(2) + b
-1 = 5 + b
b = -6
Substitute m = 5/2 and b = -6 into y = mx + b:
y = 5/2x - 6 [slope-intercept form]
6. The slope of y = -x/5 + 2 is -1/5. The negative reciprocal of -1/5 is 5.
Substitute m = 5 and (x, y) = (7, -3) into y = mx + b:
-3 = 5(7) + b
-3 = 35 + b
b = -38
Substitute m = 5 and b = -38 into y = mx + b:
y = 5x - 38 [slope-intercept form]
Learn more about the equation of parallel and perpendicular lines on:
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