Respuesta :
hello
the standard equation of a straight line is given as y = mx + b
y = y-coordinate
x = x-coordinate
m = slope
b = intercept
the points given are (3, 3) and the slope = 2 / 3
y = mx + b
y = 3
x = 3
let's substitute in our values and solve for b
[tex]\begin{gathered} y=mx+b \\ 3=\frac{2}{3}(3)+b \\ 3=2+b \\ b=3-2 \\ b=1 \end{gathered}[/tex]since we have the value of the slope, we can simply write the equation from y = mx + b to y = 2/3x + 1
[tex]y=\frac{2}{3}x+1[/tex]this is the equation of the line.
but we can further simplify this by looking for the LCM of the denominators of the independent variables
[tex]\begin{gathered} y=\frac{2}{3}x+1 \\ y=\frac{2x+3}{3} \\ \text{cross multiply both sides} \\ 3y=2x+3 \end{gathered}[/tex]the equation can be rewritten as 3y = 2x + 3
