For this case we have that by definition, the equation of the line of the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It is the slope of the line
b: It is the cut-off point with the y axis
To find the slope, we need two points, according to the table we have:
[tex](x_ {1}, y_ {1}) :( 1,50)\\(x_ {2}, y_ {2}) :( 3,40)[/tex]
The slope is:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {40-50} {3-1} = \frac {-10} {2} = -5[/tex]
Therefore, the equation is of the form:
[tex]y = -5x + b[/tex]
We substitute one of the points and find "b":
[tex]50 = -5 (1) + b\\50 = -5 + b\\50 + 5 = b\\b = 55[/tex]
Finally, the equation is of the form:
[tex]y = -5x + 55[/tex]
Answer:
[tex]m = -5\\b = 55[/tex]
