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7. Write an equation of the line that passes through (2, -1) and is parallel to the graph of y = 5x – 2. Write your final equation in slope-intercept form.
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GPT 3.5
Two lines are parallel if they have the same slope. The equation y=5x-2 is already in slope-intercept form (y=mx+b), where the slope (m) is 5.
So, the line parallel to y=5x-2 will also have a slope of 5.
To find the equation of the line that passes through (2, -1) and has a slope of 5, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the given slope.
Plugging in the values, we get:
y - (-1) = 5(x - 2)
Simplifying the equation, we have:
y + 1 = 5x - 10
Subtracting 1 from both sides, we get:
y = 5x - 11
Therefore, the equation of the line that passes through (2, -1) and is parallel to the graph of y=5x-2 is y = 5x - 11.
So, the line parallel to y=5x-2 will also have a slope of 5.
To find the equation of the line that passes through (2, -1) and has a slope of 5, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the given slope.
Plugging in the values, we get:
y - (-1) = 5(x - 2)
Simplifying the equation, we have:
y + 1 = 5x - 10
Subtracting 1 from both sides, we get:
y = 5x - 11
Therefore, the equation of the line that passes through (2, -1) and is parallel to the graph of y=5x-2 is y = 5x - 11.
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