Question

Choose the point-slope form of the equation below that represents the line that passes through the point (−1, 6) and has a slope of −3. A.y − 6 = −3x − 3 B.y − 6 = −3(x + 1) C.y = −3x + 3 D.3x + y = 3

Answer 1

The correct answer is option B.

Explanation:

Two point form of the equation:

`(y-y_1)=(y_2-y_1)/(x_2-x_1)* (x-x_1)`

`(y_2-y_1)/(x_2-x_1)=Slope=m`

`(y-y_1)=m* (x-x_1)`

A line passing through the point (-1,6) with slope ,m = -3.

The equation of the line will be:

`y-6=(-3)(x-(-1))=(-3)(x+1)`

Hence, the correct answer is option B.

Answer 2

point slope form of the equation can be written as follows
y - y₁ = m (x - x₁)
y and x are the 2 variables , m is the slope and x₁ and y₁ are the respective coordinates for the given point
in this format a point of a line and the slope of the line are given. using this information we can write down the point - slope formula for the graph
since a point has been given we know the x₁ and y₁ coordinates.
These are the coordinates of the given point (-1,6)
x₁ = -1
y₁ = 6
slope has been given as -3, m = -3
substituting these values in the formula,
y - y₁ = m (x - x₁)
y - 6 = -3 (x - (-1))
y - 6 = -3 (x + 1)
answer is B.