The equation of a line with a given slope (m) and passing through a given point (x₁, y₁) can be found using the point-slope form:
y - y₁ = m(x - x₁)
Let's calculate the equations for each given point and slope:
1) (–3, 4) with m = 2:
Using the point-slope form, we have:
y - 4 = 2(x - (-3))
y - 4 = 2(x + 3)
y - 4 = 2x + 6
y = 2x + 10
2) (3, –4) with m = 2:
Again, using the point-slope form, we have:
y - (-4) = 2(x - 3)
y + 4 = 2(x - 3)
y + 4 = 2x - 6
y = 2x - 10
3) (–3, –4) with m = 2:
Once again, using the point-slope form, we have:
y - (-4) = 2(x - (-3))
y + 4 = 2(x + 3)
y + 4 = 2x + 6
y = 2x + 2
Therefore, the correct equations for each given point and slope are:
(–3, 4) with m = 2: y = 2x + 10
(3, –4) with m = 2: y = 2x - 10
(–3, –4) with m = 2: y = 2x + 2