Question

help please I get y=mx+b but I'm not sure how to do this

Answer 1

(3,4)  (9,7)

to find the slope

m = (y2-y1)/(x2-x1)

  = (7-4)/(9-3)

3/6

1/2

The slope is 1/2

point slope form

y-y1 = m(x-x1)

y-4 = 1/2(x-3)

distribute

y-4 = 1/2x -3/2

add 4 to each side

y = 1/2 x -3/2 + 4

y = 1/2 x -3/2 + 8/2

y = 1/2 x + 5/2

this is in slope intercept form

Answer 2

y = $\frac{1}{2}$ x + $\frac{5}{2}$

the equation of a line in slope-intercept form is

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

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (3, 4 ) and (x₂, y₂ ) = (9, 7 )

m = $\frac{7-4}{9-3}$ = $\frac{3}{6}$ = $\frac{1}{2}$

y = $\frac{1}{2}$ x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (3, 4 ) then

4 = $\frac{3}{2}$ + c ⇒ c = $\frac{5}{2}$

y = $\frac{1}{2}$ x + $\frac{5}{2}$ ← equation in slope-intercept form