Question

Find the equation of line with points (3, 3) that passes through a slope of 2/3

Answer 1

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

`\begin{gathered} y=mx+b \\ 3=(2)/(3)(3)+b \\ 3=2+b \\ b=3-2 \\ b=1 \end{gathered}`

since we have the value of the slope, we can simply write the equation from y = mx + b to y = 2/3x + 1

`y=(2)/(3)x+1`

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

`\begin{gathered} y=(2)/(3)x+1 \\ y=(2x+3)/(3) \\ \text{cross multiply both sides} \\ 3y=2x+3 \end{gathered}`

the equation can be rewritten as 3y = 2x + 3