Question

trapezoids JKLM is shown below. The coordinates of J,K,L,M, are (-5, -7), (5,-7), (3-4) and (-2,4), respectively. write an equation for KL in slope intercept form.

Answer 1

Question:

Solution:

To write an equation for a line, we need a point and direction of the line. The direction is represented by the slope. Now, the slope-intercept form of a line is given by the following equation:

`y\text{ = mx+b}`

where m is the slope of a line and b is the y-intercept. Now, to find the slope m of this line we apply the following formula:

`m\text{ = }(Y2-Y1)/(X2-X1)`

where (X1,Y1) and (X2,Y2) are points on the line. In this case, we can take the points:

(X1,Y1)= (3,4)

(X2,Y2)=(5,-7)

thus, the slope of the line KL is:

`m\text{ = }(Y2-Y1)/(X2-X1)=\text{ }(-7-4)/(5-3)\text{ =}(-11)/(2)=\text{ -}(11)/(2)`

thus, the provisional equation of the line is:

`y\text{ = -}(11)/(2)x+b`

now, to find b, we can take any point on the line and replace it in the above equation; then, solve for b. For example, we can take (x,y)=(3,4), thus:

`4\text{ = -}(11)/(2)(3)+b`

this is equivalent to:

`4\text{ = -}(33)/(2)+b`

solving for b, we get:

`b=\text{ 4+}(33)/(2)=((2)(4)+33)/(2)=(8+33)/(2)=(41)/(2)`

then

`b=\text{ }(41)/(2)`

we can conclude that the slope-intercept form of the line KL is:

`y\text{ = -}(11)/(2)x+(41)/(2)`

where x varies on the interval:

`\lbrack3,5\rbrack`