Question

F(-1) = 7 f(2) = -5 Slope: Point-Slope Form:

Answer 1

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

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

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

`Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=(y_2-y_1)/(x_2-x_1)`

For this question,

(x₁, y₁) and (x₂, y₂) are (-1, 7) and (2, -5)

`\text{Slope = }(-5-7)/(2-(-1))=(-12)/(2+1)=(-12)/(3)=-4`

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)

Hope this Helps!!!