Plot the points (1, 3) and (6, 10) and draw the line through them. Answer the fo
ID: 2896516 • Letter: P
Question
Plot the points (1, 3) and (6, 10) and draw the line through them. Answer the following questions: Does the point (3, 6) line up with the two given points? Why or why not? (An answer relying on visual criteria doesn't count.) What does x have to be so (x, 12) lines up with the two given points? Write down an equation whose solution set is this line. That is, what condition do the coordinates x, y of a point have to meet in order that the point lines up with (1, 3) and (6, 10)? Put the equation you've written in slope-intercept form.Explanation / Answer
(1) The point (3,6) would line up with the two point if and only if (3,6) lies on the straight line joining (1,3) and (6,10) .
That is when straight line joining with (1,3) -(3,6) and (3,6)-(6,10) would coincide .
That is when their slopes are equal
Now , (6-3)/(3-1) = 3/2 and (10 - 3)/(6-1)=7/5 .
Therefore as they are not equal (3,6)does not line up with the two points.
2.Similarly (x,12) woul line up with the two points if and only if
(12-10)/(x-6) = (10-3)/(6-1)
=> 2/(x-6) = 7/5
=> x= 6+10/7 = 52/7 .
3. The equation of the straight line passing throuh the two points is ,
(y-3)/(x-1) = (10-3)/(6-1)= 7/5
=> 7(x-1) = 5(y-3)
=> 7x-5y + 8 =0
This is the equation.
4.The equation in the slope-intercept form is given by,
y = 7/5x + 8/5 . slope is 7/5 , intercept is 8/5 .