Question

O GRAPHS AND FUNCTIONSWriting the equation of the line through two given pointsFind an equation for the line below.

Answer 1

The equation of the line in slope-point form is

y + 3 = 0.2 (x + 4)

Thw equation of the line in slope-intercept form is

y = 0.2x - 2.2

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

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 (-4, -3) and (6, -1)

`\text{Slope = }(-1-(-3))/(6-(-4))=(-1+3)/(6+4)=(2)/(10)=0.2`

Recall,

y - y₁ = m (x - x₁)

(x₁, y₁) = (-4, -3)

x₁ = -4

y₁ = -3

m = Slope = 0.2

y - y₁ = m (x - x₁)

y - (-3) = 0.2 (x - (-4))

y + 3 = 0.2 (x + 4)

y + 3 = 0.2x + 0.8

y = 0.2x + 0.8 - 3

y = 0.2x - 2.2

Hope this Helps!!!