Question

Find the equation of the line passing through point (3,5) and with a slope ⅓

Answer 1

hello

we are given 1 point with x and y co-ordinate and a slope, we can easily write down the equation of the line

standard equation of a straight line is

`\begin{gathered} y=mx+c \\ m=\text{slope} \\ c=\text{intercept} \end{gathered}`

to solve this problem, we need to find the intercept first

substitute the x and y co-ordinates in the equation

`\begin{gathered} y=mx+c \\ m=(1)/(3) \\ y=5 \\ x=3 \\ 5=(1)/(3)(3)+c \\ 5=1+c \\ c=4 \end{gathered}`

we know our intercept is equal to 4 and we can proceed to write out our equation

`y=(1)/(3)x+4`

we can leave it this way or multiply through by 3

`3y=x+12`