Question

Determine the equation of each line

Answer 1

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 = - $\frac{3}{4}$ and c = 6, hence

y = - $\frac{3}{4}$ 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 = $\frac{7-3}{4+1}$ = $\frac{4}{5}$, hence

y = $\frac{4}{5}$ x + c ← is the partial equation

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

using (- 1, 3 ), then

3 = - $\frac{4}{5}$ + c → c = 3 + $\frac{4}{5}$ = $\frac{19}{5}$

y = $\frac{4}{5}$ x + $\frac{19}{5}$ ← equation of line