1. The equation in slope-intercept form is: y = -3/2x + 7/2
2. y = -3/2x - 18
3. Both lines have the same slope, they are therefore parallel.
Two lines that are parallel will have the same slope (m), and is represented by the equation in slope-intercept form as, y = mx + b.
1. Rewrite 3x + 2y = 4 in slope-intercept form:
2y = -3x + 4
y = -3x/2 + 4/2
y = -3/2x + 2
The slope is -3/2. Therefore, the slope (m) of the line that passes through (-1, 5) would be -3/2.
Substitute m = -3/2, and (a, b) = (-1, 5) into y - b = m(x - a):
y - 5 = -3/2(x - (-1))
y - 5 = -3/2(x + 1)
Rewrite in slope-intercept form:
2(y - 5) = -3(x + 1)
2y - 10 = -3x - 3
2y = -3x - 3 + 10
2y = -3x + 7
y = -3x/2 + 7/2
y = -3/2x + 7/2
2. The slopes of perpendicular lines are negative reciprocal to each other.
Rewrite 2x + 3y = 4
3y = -2x + 4
y = -2/3x + 4/3
The slope of the ine that passes (-2, 15) would be -3/2.
Substitute (a, b) = (-2, 15), and m = -3/2 into y - b = m(x - a):
y - 15 = -3/2(x - (-2))
y - 15 = -3/2x - 3
y = -3/2x - 3 - 15
y = -3/2x - 18
Therefore, the equation in slope-intercept form of the line that passes through (-2, 15) is: y = -3/2x - 18.
3. Given the equations, 2x – y = −1 and 4x – 2y = 6:
Rewrite in slope-intercept form and find their slope
2x - y = -1
-y = -2x - 1
y = 2x + 1 (slope if 2)
4x - 2y = 6
-2y = -4x + 6
y = -4x/-2 + 6/-2
y = 2x - 3 (slope is 2)
Both lines are therefore, parallel.
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