Question

For the straight line defined by the points (3,51) and (5,83), determine the slope (m) and y-intercept (b). Do not round the answers. m= b=

Answer 1

m = 16 , b = 3

Explanation:

the equation of a line in slope- intercept form is

y = mx + b ( m is the slope and b the y- intercept )

calculate slope m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (3, 51 ) and (x₂, y₂ ) = (5, 83 )

substitute these values into the formula for m

m =
`(83-51)/(5-3)` =
`(32)/(2)` = 16 , then

y = 16x + b ← is the partial equation

to find b substitute either of the 2 given points into the partial equation

using (3, 51 )

51 = 16(3) + b = 48 + b ( subtract 48 from both sides )

3 = b

y = 16x + 3 ← is in slope- intercept form

with slope m = 16 and y- intercept b = 3