Answer
y - 3 = -0.5 (x + 3)
To silmplify, we multiply through by 2
2y - 6 = -1 (x + 3)
2y - 6 = -x - 3
2y = -x - 3 + 6
2y = -x + 3
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
So, we need to calculate the slope and use one of the points given as (x₁, y₁).
To calculate the slope,
For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as
[tex]Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex]
For this question,
(x₁, y₁) and (x₂, y₂) are (-3, 3) and (9, -3)
x₁ = -3
y₁ = 3
x₂ = 9
y₂ = -3
[tex]\text{Slope = }\frac{-3-3}{9-(-3)}=\frac{-6}{9+3}=\frac{-6}{12}=-\frac{1}{2}=-0.5[/tex]
Using the first point given as (x₁, y₁)
(x₁, y₁) = (-3, 3)
x₁ = -3, y₁ = 3
Recall that
y - y₁ = m (x - x₁)
m = -0.5
y - 3 = -0.5 (x - (-3))
y - 3 = -0.5 (x + 3)
To silmplify, we multiply through by 2
2y - 6 = -1 (x + 3)
2y - 6 = -x - 3
2y = -x - 3 + 6
2y = -x + 3
Hope this Helps!!!
