Question

Determine the point-slope form of the linear equation from its graph.

Answer 1

Question:

Solution:

The slope-intercept form of the line is given by the following equation:

`y\text{ = mx + b}`

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:

`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) = (797, 1171)

(X2,Y2) = (1122, 1111)

now, replace this data into slope equation:

`m\text{ = }(Y2-Y1)/(X2-X1)=\text{ }\frac{1111\text{ - 1171}}{1122-797}\text{ = }(-60)/(325)=\text{ }(-12)/(65)`

then, temporarily we have that the equation of the given line is

`y\text{ = -}(12)/(65)x\text{ + b}`

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:

`1171\text{ = -}(12)/(65)(797)\text{ + b}`

this is equivalent to say:

`b=1171\text{ +}(12)/(65)(797)=\text{ 1318,138}\approx\text{ 1318,1}4`

then, we can conclude that the slope-intercept form for the given line is:

`y\text{ = -}(12)/(65)x\text{ + }1318,14`