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Find the equation of the line that passes through the point (3; -5) and has slope 7/3

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Answer to a math question Find the equation of the line that passes through the point (3; -5) and has slope 7/3

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Bud
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96 Answers
Solution:
1. Use the point-slope form of a line equation:
- The point-slope form is: y - y_1 = m(x - x_1)
- Given point: (x_1, y_1) = (3, -5)
- Given slope: m = \frac{7}{3}

2. Substitute the given values into the point-slope form:
- y - (-5) = \frac{7}{3}(x - 3)
- Simplify the equation: y + 5 = \frac{7}{3}(x - 3)

3. Distribute the slope on the right side:
- y + 5 = \frac{7}{3}x - \frac{21}{3}
- Simplify: y + 5 = \frac{7}{3}x - 7

4. Isolate y to find the equation in slope-intercept form (y = mx + b):
- Subtract 5 from both sides: y = \frac{7}{3}x - 7 - 5
- Simplify: y = \frac{7}{3}x - 12

5. The equation of the line in slope-intercept form is:
y = \frac{7}{3}x - 12

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