1. write an equation of the line that passes through the point and has the given slope. write the equation in slope-intercept form.
a. (3,2), m=1/2
b. (-3,2), m=1/2
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answers:
a. y=1/2x + 1/2
b. y=1/2x + 7/2
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2. write an equation of the line that is parallel to the given line and passes through the given point.
a. y=-3x+2, (2,3)
b. y=1/2x-5, (-3,-1)
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answers:
a. y=-3x + 9
b. y=1/2x+1/2
Please check my answers and tell me if they're correct.. Thanks!
All correct!
Thsnks again!! (=
You're welcome, Rachel.
Let's go through each question step by step to check your answers:
1a. To find the equation of a line passing through the point (3,2) with a slope of 1/2, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m represents the slope and b represents the y-intercept.
Using the given point (3,2), we can substitute the x and y values into the equation to find the y-intercept, b.
2 = (1/2)(3) + b
2 = 3/2 + b
b = 2 - 3/2
b = 1/2
So the equation of the line is y = (1/2)x + 1/2.
1b. Similarly, for the point (-3,2) with a slope of 1/2, we can use the same approach. Substituting the x and y values into the equation, we find:
2 = (1/2)(-3) + b
2 = -3/2 + b
b = 2 + 3/2
b = 7/2
Therefore, the equation of the line is y = (1/2)x + 7/2.
2a. To find the equation of a line parallel to y = -3x + 2 passing through the point (2,3), we know that parallel lines have the same slope.
The given line has a slope of -3, so the parallel line will also have a slope of -3.
Using the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope, we can substitute the values into the equation to find the equation of the line:
y - 3 = -3(x - 2)
y - 3 = -3x + 6
y = -3x + 9
So the equation of the line is y = -3x + 9.
2b. Following the same procedure, for the line y = 1/2x - 5 passing through (-3, -1), we substitute the values into the equation:
y - (-1) = (1/2)(x - (-3))
y + 1 = (1/2)(x + 3)
y + 1 = (1/2)x + 3/2
y = (1/2)x + 1/2
Thus, the equation of the line is y = (1/2)x + 1/2.
Therefore, your answers for all the questions are correct:
1a. y = 1/2x + 1/2
1b. y = 1/2x + 7/2
2a. y = -3x + 9
2b. y = 1/2x + 1/2