Question

What is an equation of the line that passes through the points (3,4) and (1,-2)Please answer in fully reduced form

Answer 1

The equation of the line in the point-slope form is

y - 4 = 3 (x - 3)

The equation of the line in slope-intercept form is

y = 3x - 5

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

So, to write the equation of this line, we just need to calculate the slope and use one of the two points given to write 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

`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 (3, 4) and (1, -2)

x₁ = 3

y₁ = 4

x₂ = 1

y₂ = -2

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

Recall that

y - y₁ = m (x - x₁)

m = Slope = 3

Point = (x₁, y₁) = (3, 4)

x₁ = 3

y₁ = 4

y - y₁ = m (x - x₁)

y - 4 = 3 (x - 3)

y - 4 = 3x - 9

y = 3x - 9 + 4

y = 3x - 5