Question
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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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
1. Use the point-slope form of a line equation:
- The point-slope form is:
- Given point:
- Given slope:
2. Substitute the given values into the point-slope form:
-
- Simplify the equation:
3. Distribute the slope on the right side:
-
- Simplify:
4. Isolate y to find the equation in slope-intercept form (y = mx + b):
- Subtract 5 from both sides:
- Simplify:
5. The equation of the line in slope-intercept form is:
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