Answer:
see explanation
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
(a)
here m = - [tex]\frac{3}{4}[/tex] and c = 6, hence
y = - [tex]\frac{3}{4}[/tex] x + 6 ← equation of line
(b)
here m = 6, hence
y = 6x + c ← is the partial equation
to find c substitute (2, - 6 ) into the partial equation
- 6 = 12 + c ⇒ c = - 6 - 12 = - 18
y = 6x - 18 ← equation of line
(c)
to calculate m use the gradient formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (- 1, 3) and (x₂, y₂ ) = (4, 7)
m = [tex]\frac{7-3}{4+1}[/tex] = [tex]\frac{4}{5}[/tex], hence
y = [tex]\frac{4}{5}[/tex] x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (- 1, 3 ), then
3 = - [tex]\frac{4}{5}[/tex] + c → c = 3 + [tex]\frac{4}{5}[/tex] = [tex]\frac{19}{5}[/tex]
y = [tex]\frac{4}{5}[/tex] x + [tex]\frac{19}{5}[/tex] ← equation of line
