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Sagot :
Answer
Slope: -4
Point-Slope Form: y - 7 = -4 (x + 1)
We can then simplify this further to get
y - 7 = -4 (x + 1)
y - 7 = -4x - 4
y = -4x - 4 + 7
y = -4x + 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
Note that f(-1) = 7 represents the value of y when x = -1.
That is,
f(-1) = 7
x = -1
y = 7
Point = (-1, 7)
f(2) = -5
x = 2
y = -5
Point = (2, -5)
So, we can calculate the slope now and use one of these points to write the equation of the line.
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, 7) and (2, -5)
[tex]\text{Slope = }\frac{-5-7}{2-(-1)}=\frac{-12}{2+1}=\frac{-12}{3}=-4[/tex]Slope = -4
Recall that
y - y₁ = m (x - x₁)
m = slope = -4
Point = (x₁, y₁) = (-1, 7)
x₁ = -1
y₁ = 7
y - y₁ = m (x - x₁)
y - 7 = -4 (x - (-1))
y - 7 = -4 (x + 1)
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