Question

What is the equation of the line through the origin and (3, 4)? helllp

Answer 1

The general line equation in slope-intercept form is given by

`y=mx+b`

where b is the y-intercept and m is the slope. In our case, we have the points

`\begin{gathered} (x_1,y_1)=(0,0) \\ (x_2,y_2)=(3,4) \end{gathered}`

and the slope m is given by

`m=(y_2-y_1)/(x_2-x_1)`

by substituting our point into this formula,we get

`\begin{gathered} m=(4-0)/(3-0) \\ m=(4)/(3) \end{gathered}`

then, our line equation has the form

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

We can find b by substituting point (0,0) in this last equation. It yields,

`\begin{gathered} 0=(4)/(3)(0)+b \\ b=0 \end{gathered}`

Then, the line equation is

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

which corresponds to option A.