Answer:
Step-by-step explanation:
For (a), you will use that 2 points that are closest to lying on the line which are the points located at (1, 14) and (7, 7).
For (b), you will use those 2 points to find the slope of the line using the slope formula:
[tex]m=\frac{7-14}{7-1}=\frac{-7}{6}=-1.167[/tex]
For (c), you will use point-slope form to write the equation. Point-slope form is
[tex]y-y_1=m(x-x_1)[/tex] where x and y stay x and y in the equation and x1 and y1 are replaced with one of the coordinates. Let's use (7, 7). Keep in mind that IT DOESN'T MATTER WHICH POINT YOU PICK...YOU WILL GET THE SAME EQUATION WITH EITHER ONE! And this is because both those points lie on the same line...the line for which we will write the equation.
We have m = -1.167, y = 7 and x = 7:
y - 7 = -1.167(x - 7)
That's the point-slope form of the line, but rarely is it ever left in that form. I've only seen it left in point-slope form in calculus. Most of the time, from point-slope form, you are asked to put it into slope-intercept form, and here is no exception. Putting the equation into slope-intercept form is the same thing as solving it for y. So let's get y all by itself on one side of the equals sign and everything else over on the other side. We also of course need to distribute into the parenthesis:
y - 7 = -1.167x + 8.169 and
y = -1.167 + 8.169 + 7 so
y = -1.167 + 15.169
That's your equation in slope-intercept form, so you're done!
