Question

Find a point-slope equation for a line containing the given point and having the given slope.

1. (-5, -6), m = 2

2. (-7, 2), m = 3

3. (3, 5), m = 2

4. (6, -2), m = -3

5. (5, -2), m = 2

6. (7, 0), m = 4

7. (0, 9), m = -2

8. (1, 3), m = 1

Answer 1

The point-slope equations for the given points and slopes are:
1. y + 6 = 2x + 10
2. y - 2 = 3x + 21
3. y - 5 = 2x - 6
4. y + 2 = -3x + 18
5. y + 2 = 2x - 10
6. y = 4x - 28
7. y - 9 = -2x
8. y - 3 = x - 1

Step-by-step explanation:

To find the point-slope equation for a line, we use the formula y - y1 = m(x - x1), where (x1, y1) is the given point and m is the given slope.

1. For (-5, -6) and m = 2, the equation is y - (-6) = 2(x - (-5)) which simplifies to y + 6 = 2x + 10.
2. For (-7, 2) and m = 3, the equation is y - 2 = 3(x - (-7)) which simplifies to y - 2 = 3x + 21.
3. For (3, 5) and m = 2, the equation is y - 5 = 2(x - 3) which simplifies to y - 5 = 2x - 6.
4. For (6, -2) and m = -3, the equation is y - (-2) = -3(x - 6) which simplifies to y + 2 = -3x + 18.
5. For (5, -2) and m = 2, the equation is y - (-2) = 2(x - 5) which simplifies to y + 2 = 2x - 10.
6. For (7, 0) and m = 4, the equation is y - 0 = 4(x - 7) which simplifies to y = 4x - 28.
7. For (0, 9) and m = -2, the equation is y - 9 = -2(x - 0) which simplifies to y - 9 = -2x.
8. For (1, 3) and m = 1, the equation is y - 3 = 1(x - 1) which simplifies to y - 3 = x - 1.