SOLUTION:
Case:
Slope-intercept form given two points
The slope-intersecept form is used to find the line equation. In the Slope intercept equation, we need to know the slope of the line and the point where the line intersects the Y axis. Consider a straight line with an inclination of "m" and an intersection of "b". The shape equation for a straight sloped section with the slopes "m" and "b" as the y-intercept can be given as y = mx + b.
Given: The line goes through the points (8,5) and (6, 13).
Required: To use the points to form an equation in the slope-intercept form.
Method:
First we use the points (8,5) and (6, 13) into the form:
y = mx + b.
5 = 8m + b..........(1)
13= 6m +b...........(2)
Subtracting equations (1) from (2)
13 - 5 = 6m - 8m + b - b
8 = -2m
Divide both sides by -2
m = -4.
Plug m= -4 into equation (2)
13= 6m +b.
13= 6(-4) +b
13 = -24 + b
b = 13 + 24
b = 37
Therefore the equation is:
y = mx + b, m= -4, b= 37
y= -4x + 37
slope, m= -4 AND
y-intercept, b= 37
Final answer:
The equation of the line in the slope-intercept form is:
y= -4x + 37