Question
What is the equation,in slope-intercept form, of the line that is parallel to the given line and passes through the point (0,12)?
Answers
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GPT 3.5
To find the equation of the line in slope-intercept form that is parallel to a given line and passes through a specific point, follow these steps:
1. Determine the slope of the given line. Let the slope of the given line be m.
2. Since the line we want to find is parallel to the given line, it will have the same slope as the given line. So, the slope of the line we are looking for is also m.
3. Use the point-slope form of the equation of a line: y - y1 = m(x - x1), where (x1, y1) is the given point (0,12).
4. Substitute the slope m and the point (0,12) into the point-slope form: y - 12 = m(x - 0).
5. Simplify the equation to get it into slope-intercept form (y = mx + b), by distributing the slope m: y - 12 = mx.
6. Finally, rearrange the equation to solve for y: y = mx + 12.
Therefore, the equation of the line in slope-intercept form that is parallel to the given line and passes through the point (0,12) is y = mx + 12.
1. Determine the slope of the given line. Let the slope of the given line be m.
2. Since the line we want to find is parallel to the given line, it will have the same slope as the given line. So, the slope of the line we are looking for is also m.
3. Use the point-slope form of the equation of a line: y - y1 = m(x - x1), where (x1, y1) is the given point (0,12).
4. Substitute the slope m and the point (0,12) into the point-slope form: y - 12 = m(x - 0).
5. Simplify the equation to get it into slope-intercept form (y = mx + b), by distributing the slope m: y - 12 = mx.
6. Finally, rearrange the equation to solve for y: y = mx + 12.
Therefore, the equation of the line in slope-intercept form that is parallel to the given line and passes through the point (0,12) is y = mx + 12.
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