Answer:
First, find the slope using the points (- 2, 3) and (3, - 1): m = = = - .
Next, pick a point -- for example, (- 2, 3). Using this point, h = - 2 and k = 3.
Therefore, the equation of this line is y - 3 = - (x - (- 2)), which is equivalent to y - 3 = - (x + 2).
Check using the point (3, -1): -1 - 3 = - (3 + 2) ? Yes.
Example 2: Write an equation of the line which passes through (3, 4) and has slope m = 5.
h = 3 and k = 4. y - 4 = 5(x - 3)
Example 3: Write an equation of the line which is parallel to the line y = 3x + 2 and passes through (- 1, 2).
m = 3, h = - 1, and k = 2.
The equation of the line is y - 2 = 3(x + 1).
Example 4: Write an equation of the line which is perpendicular to the line y - 8 = 2(x + 2) and passes through (7, 0).
The slope is the opposite reciprocal of 2: m = - . h = 7 and k = 0.
The equation of the line is y - 0 = - (x - 7), which is equivalent to y = - (x - 7).
Example 5: Write an equation of the line with slope m = 4 that passes through the point (0, 3).
m = 4, h = 0, and k = 3.
The equation of the line is y - 3 = 4x. If we move -3 to the other side--y = 4x + 3--we get the equation in slope-intercept form.