Question
Write an equation for the line that is parallel to the given line and passes through the given point.
y = 3x + 7; (2, 10)
y = 3x + 7; (2, 10)
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GPT 3.5
To find the equation of a line parallel to the given line y = 3x + 7, we know that it will have the same slope as the given line. Thus, the slope of the parallel line is also 3.
Using the point-slope form of a linear equation, y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point, we can substitute the values and find the equation of the parallel line:
y - 10 = 3(x - 2).
Expanding and simplifying:
y - 10 = 3x - 6.
Finally, rearranging the equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept:
y = 3x + 4.
Therefore, the equation of the line parallel to y = 3x + 7 and passing through the point (2, 10) is y = 3x + 4.
Using the point-slope form of a linear equation, y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point, we can substitute the values and find the equation of the parallel line:
y - 10 = 3(x - 2).
Expanding and simplifying:
y - 10 = 3x - 6.
Finally, rearranging the equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept:
y = 3x + 4.
Therefore, the equation of the line parallel to y = 3x + 7 and passing through the point (2, 10) is y = 3x + 4.
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