Answer:
Line: [tex]y=4/3x[/tex], Graph: desmos(.com)/calculator/tiptlly8xj
Step-by-step explanation:
First off, your slope is wrong. I will show you how to find the correct slope, and will make the graph.
The change in [tex]y[/tex] is [tex]16-8=8[/tex].
The change in [tex]x[/tex] is [tex]12-6=6[/tex].
That makes the slope [tex]8/6=4/3[/tex].
Recall point-slope form. That is, given a point [tex](x_{1}, y_{1})[/tex] and a slope [tex]m[/tex], the line through the given point with the given slope is of the form [tex]y-y_{1}=m(x-x_{1})[/tex].
Plugging in one of the points, (6, 8)(we could also use (12, 16)) to the point-slope equation gives the line: [tex]y-8=4/3(x-6)[/tex].
Converting to slope-intercept form([tex]y=mx+b[/tex])...
Simplifying the right hand side gives [tex]y-8=4/3x-8[/tex].
Adding [tex]8[/tex] to both sides gives the desired line, [tex]y=4/3x[/tex].
The graph is shown on Desmos in the answer.
