Question

f (4) = 13 and f (0) = 21write an equation in point slope form

Answer 1

Answer

The equation of the line in point slope form is

y - 13 = -2 (x - 4)

Simplifying this further

y - 13 = -2x + 8

y = -2x + 8 + 13

y = -2x + 21

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

The coordinates of the points on the line are given in the form

f(x) = y

f(4) = 13 means (4, 13)

f(0) = 21 means (0, 21)

So, we need to calculate the slope of the line and use one of the points given as (x₁, y₁)

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

$Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}$

(x₁, y₁) and (x₂, y₂) are (4, 13) and (0, 21)

x₁ = 4

y₁ = 13

x₂ = 0

y₂ = 21

$\text{Slope = }\frac{21-13}{0-4}=\frac{8}{-4}=-2$

m = -2

(x₁, y₁) = (4, 13)

x₁ = 4

y₁ = 13

y - y₁ = m (x - x₁)

y - 13 = -2 (x - 4)

Simplifying this further

y - 13 = -2x + 8

y = -2x + 8 + 13

y = -2x + 21

Hope this Helps!!!