What is the slope of a line passing through (3, 8) and (5, 5)?

Accepted Solution

Answer:Step-by-step explanation:bYour input is P=(3,8) and Q=(5,5). The slope of the line passing through the two points P=(x1,y1) and Q=(x2,y2) is given by m=y2βˆ’y1x2βˆ’x1. We have that x1=3, y1=8, x2=5, y2=5. Plug the given values into the formula for the slope: m=(5)βˆ’(8)(5)βˆ’(3)=βˆ’32=βˆ’32. Now, the y-intercept is b=y1βˆ’mβ‹…x1 (or b=y2βˆ’mβ‹…x2, the result is the same). b=8βˆ’(βˆ’32)β‹…(3)=252. Finally, the equation of the line can be written in the form y=mx+b. y=βˆ’32x+252. Answer: The slope of the line is m=βˆ’32=βˆ’1.5. The y-intercept is (0,252)=(0,12.5). The equation of the line in the slope-intercept form is y=βˆ’32x+252=βˆ’1.5x+12.5