Answer
Option D is correct.
y + 9 = ½ (x + 4)
Option C is correct.
y = -3x + 5
Option B is correct.
y = -4x + 9
Step-by-step explanation
The general form of the equation in point-slope form is
y - y₁ = m (x - x₁)
where
y = y-coordinate of a point on the line.
y₁ = This refers to the y-coordinate of a given point on the line
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
x₁ = x-coordinate of the given point on the line
For this question,
Slope = m = ½
Given point, (x₁, y₁) = (-4, -9)
x₁ = -4, y₁ = -9
y - y₁ = m (x - x₁)
y - (-9) = ½ [x - (-4)]
y + 9 = ½ (x + 4)
For the second question, recall that the slope-point form of the equation is
y - y₁ = m (x - x₁)
For this question,
Slope = m = -3
Given point, (x₁, y₁) = (2, -1)
x₁ = 2, y₁ = -1
y - y₁ = m (x - x₁)
y - (-1) = -3 (x - 2)
y + 1 = -3x + 6
y = -3x + 6 - 1
y = -3x + 5
For the third question, we should note that two parallel lines have the same slopes.
The slope and y-intercept form of the equation of a straight line is given as
y = mx + b
where
y = y-coordinate of a point on the line.
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
b = y-intercept of the line.
The equation of the line provided is 4x + y = 5
So, putting it in the form of y = mx + b
4x + y = 5
y = -4x + 5
We can see that the slope = m = -4 and the y-intercept = b = 5
So, amongst the options, we will pick the line with slope = -4 too.
And that is option B where y = -4x + 9
Hope this Helps!!!