Question:
Solution:
The slope-intercept form of the line is given by the following equation:
[tex]y\text{ = mx + b}[/tex]
where m is the slope of the line and b is the y-coordinate of the y-intercept of the line. Now, to find the slope of a line we use the following equation:
[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) = (797, 1171)
(X2,Y2) = (1122, 1111)
now, replace this data into slope equation:
[tex]m\text{ = }\frac{Y2-Y1}{X2-X1}=\text{ }\frac{1111\text{ - 1171}}{1122-797}\text{ = }\frac{-60}{325}=\text{ }\frac{-12}{65}[/tex]
then, temporarily we have that the equation of the given line is
[tex]y\text{ = -}\frac{12}{65}x\text{ + b}[/tex]
to find b, replace any point (x,y) on the line, in the above equation, and solve for b. For example, take (x,y) = (797, 1171), then we get:
[tex]1171\text{ = -}\frac{12}{65}(797)\text{ + b}[/tex]
this is equivalent to say:
[tex]b=1171\text{ +}\frac{12}{65}(797)=\text{ 1318,138}\approx\text{ 1318,1}4[/tex]
then, we can conclude that the slope-intercept form for the given line is:
[tex]y\text{ = -}\frac{12}{65}x\text{ + }1318,14[/tex]
