Question

-matrices- Use determinants to find the equation of the line passing through (12,4) and (4,19).

Answer 1

To determine the equation of the line that passes through the points (12,4) and (4,19), the first step is to use the coordinates of both points to calculate the slope of the line using the formula:

`m=(y_2-y_1)/(x_2-x_1)`

Where

(x₁,y₁) are the coordinates of one of the points

(x₂,y₂) are the coordinates of the second point

Use (4,19) as (x₁,y₁) and (12,4) as (x₂,y₂)

`\begin{gathered} m=(4-19)/(12-4) \\ m=(-15)/(8) \end{gathered}`

The slope of the line is m=-15/8

Next, use the point-slope form to determine the equation of the line

`y-y_1=m(x-x_1)`

m is the slope of the line

(x₁,y₁) are the coordinates of one point

Use one of the points, for example, (12,4) and the slope m=-15/8

`y-4=-(15)/(8)(x-12)`

You can write the equation in slope-intercept form:

-Distribute the multiplication in the parentheses term:

`\begin{gathered} y-4=-(15)/(8)\cdot x-(-(15)/(8))\cdot12 \\ y-4=-(15)/(8)x+(45)/(2) \end{gathered}`

-Add 4 to both sides of the equation

`\begin{gathered} y-4+4=-(15)/(8)x+(45)/(2)+4 \\ y=-(15)/(8)x+(53)/(2) \end{gathered}`