Question

Write an equation in point slope form of a line that passes through the given point and has the given slope.
1.) (2,7); m=-4
2.) (12,5); m=-3
3.) (4,-5) ; m=6

Answer 1

To write the equation of a line in point-slope form, we use the formula:

\[ y - y_1 = m(x - x_1) \]

where \( (x_1, y_1) \) is the given point and \( m \) is the slope.

1.) For the point (2, 7) and slope \( m = -4 \):
\[
y - 7 = -4(x - 2)
\]

2.) For the point (12, 5) and slope \( m = -3 \):
\[
y - 5 = -3(x - 12)
\]

3.) For the point (4, -5) and slope \( m = 6 \):
\[
y + 5 = 6(x - 4)
\]

So the equations in point-slope form for each case are:
1.) \( y - 7 = -4(x - 2) \)
2.) \( y - 5 = -3(x - 12) \)
3.) \( y + 5 = 6(x - 4) \)