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:
[tex]y\text{ = mx+b}[/tex]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:
[tex]m\text{ = }\frac{Y2-Y1}{X2-X1}[/tex]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:
[tex]m\text{ = }\frac{Y2-Y1}{X2-X1}=\text{ }\frac{-7-4}{5-3}\text{ =}\frac{-11}{2}=\text{ -}\frac{11}{2}[/tex]thus, the provisional equation of the line is:
[tex]y\text{ = -}\frac{11}{2}x+b[/tex]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:
[tex]4\text{ = -}\frac{11}{2}(3)+b[/tex]this is equivalent to:
[tex]4\text{ = -}\frac{33}{2}+b[/tex]solving for b, we get:
[tex]b=\text{ 4+}\frac{33}{2}=\frac{(2)(4)+33}{2}=\frac{8+33}{2}=\frac{41}{2}[/tex]then
[tex]b=\text{ }\frac{41}{2}[/tex]we can conclude that the slope-intercept form of the line KL is:
[tex]y\text{ = -}\frac{11}{2}x+\frac{41}{2}[/tex]where x varies on the interval:
[tex]\lbrack3,5\rbrack[/tex]
