Question

Write an equation of the line that passes through each pair of point y=mx+b

Answer 1

`y=-(2)/(3)x+4`

Step-by-step explanation

Step 1

find the slope

when yo know 2 points of a lines, P1 and P2, you can find the slope by using:

`\begin{gathered} \text{slope}=\frac{change\text{ in y}}{\text{change in x}}=(y_2-y_1)/(x_2-x_1) \\ \text{where} \\ P1(x_1,y_1) \\ P2(x_2,y_2) \end{gathered}`

then, let

P1(6,0)

P2(0,4)

replace

`\begin{gathered} \text{slope}=(y_2-y_1)/(x_2-x_1) \\ slope=(4-0)/(0-6)=(4)/(-6)=-(2)/(3) \end{gathered}`

Step 2

find the equation of the line,

`\begin{gathered} y-y_1=slope(x-x_1) \\ \text{replace} \\ y-0=-(2)/(3)(x-6) \\ y=-(2)/(3)x+(12)/(3) \\ y=-(2)/(3)x+4 \end{gathered}`

so , the equation of the lines is

`y=-(2)/(3)x+4`

where -2/3 is the slope, and 4 is the y-intercept

I hope this helps you