Question

Graph a line with of 1/4 that contains the point 6,3

Answer 1

We have to graph a line with a slope of 1/4 that contains the point (6,3).

We can write the point slope equation for this line as:

`\begin{gathered} y-y_0=m(x-x_0) \\ y-3=(1)/(4)(x-6) \end{gathered}`

We can rearrange this equation as:

`\begin{gathered} y-3=(1)/(4)(x-6) \\ y-3=(1)/(4)x-(6)/(4) \\ y=(1)/(4)x-(3)/(2)+3 \\ y=(1)/(4)x+((-3+6))/(2) \\ y=(1)/(4)x+(3)/(2) \end{gathered}`

The y-intercept is y=3/2 and for every 4 units of increase in x, y increases in one unit:

We can verify if (6,3) is included in the line by looking at the graph or replacing x and y in the equation and verifying if it is true:

`\begin{gathered} 3=(1)/(4)(6)+(3)/(2) \\ 3=(3)/(2)+(3)/(2) \\ 3=(6)/(2) \\ 3=3\longrightarrow\text{true} \end{gathered}`