Answer:
y = - 2 + [tex]\frac{1}{3}[/tex] x
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 )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, - 2) and (x₂, y₂ ) = (6, 0) ← 2 points on the line
m = [tex]\frac{0+2}{6-0}[/tex] = [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]
The line crosses the y- axis at (0, - 2 ) ⇒ c = - 2
y = [tex]\frac{1}{3}[/tex] x - 2 , or
y = - 2 + [tex]\frac{1}{3}[/tex] x
Answer:
Proof
Step-by-step explanation:
"The y-intercept is - 2" and now I think the best way to prove the gradient is to prove it mathematically taking coordinates of the line and using:
[tex]m = \frac{y - y}{x - x} [/tex]
So I'll take the coordinates (6,0) and (0,-2) and substitute them in the formula for the gradient.
[tex]m = \frac{ - 2 - 0}{0 - 6} = \frac{ - 2}{ - 6} = \frac{1}{3} [/tex]
I hope this helps.
