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Sagot :
Answer
The equation of the line in point-slope form is
y - 6 = -0.5 (x + 1)
We can now simplify further
y - 6 = -0.5x - 0.5
y = -0.5x - 0.5 + 6
y = -0.5x + 5.5
This is the slope-intercept form
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 can use any one of the two points as the point in the equation.
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 (-1, 6) and (1, 5)
[tex]\text{Slope = }\frac{5-6}{1-(-1)}=\frac{-1}{1+1}=\frac{-1}{2}=-0.5[/tex]Recall
y - y₁ = m (x - x₁)
m = slope = -0.5
Point = (x₁, y₁) = (-1. 6)
x₁ = -1
y₁ = 6
y - y₁ = m (x - x₁)
y - 6 = -0.5 (x - (-1))
y - 6 = -0.5 (x + 1)
We can now simplify further
y - 6 = -0.5x - 0.5
y = -0.5x - 0.5 + 6
y = -0.5x + 5.5
Hope this Helps!!!
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