Question

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

Answer 1

$y=-\frac{2}{3}x+4$

Explanation

Step 1

find the slope

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

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

then, let

P1(6,0)

P2(0,4)

replace

$\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ slope=\frac{4-0}{0-6}=\frac{4}{-6}=-\frac{2}{3} \end{gathered}$

Step 2

find the equation of the line,

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

so , the equation of the lines is

$y=-\frac{2}{3}x+4$

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

I hope this helps you