Question 1209474
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The two given points are (4,55) and (6,83).  We need to find the slope m and the y-intercept b.<br>
(1) Finding the slope<br>
Informally....<br>
Going from (4,55) to (6,83) we move 2 units (6-4) to the right (positive direction) and 28 units (83-55) up (positive direction).  So the slope is 28/2 = 14.<br>
Formally....<br>
slope = rise/run = change in y divided by change in x<br>
{{{(y2-y1)/(x2-x1)=(83-55)/(6-4)=28/2=14}}}<br>
ANSWER #1: the slope is m=14<br>
(2) Finding the y-intercept<br>
Informally....<br>
The y-intercept is the y value when x is 0.  From the first point (4,55) we need to move 4 units to the left to get to where x is 0.  In moving 2 units to the right from (4,55) to (6,83) we moved up 28 units; moving 4 units to the left is twice as far as moving 2 units to the right, and in the opposite direction.  So we need to move 2*28=56 units down (in the y direction) from (4,55) to reach the y-axis.  56 units down from y=55 puts us at y=-1. So the y-intercept is -1.<br>
Formally....<br>
The equation is y=mx+b, and we have determined that the slope m is 14.  Using that equation with the x and y coordinates of the first point and the slope of 14....<br>
{{{55=14(4)+b}}}
{{{55=56+b}}}
{{{55-56=b}}}
{{{b=-1}}}<br>
ANSWER #2: the y-intercept is -1<br>