y-intercept = (0, - 2) and x-intercept = ( [tex]\frac{3}{2}[/tex], 0)
the equation of a line in slope-intercept form is
y = mx + c ( m is the slope and c the y-intercept )
The 3 given points all lie on the same line
calculate m using the gradient formula
m = ( y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (3, 6 ) and (x₂, y₂ ) = (6, 10)
m = [tex]\frac{10-6}{6-3}[/tex] = [tex]\frac{4}{3}[/tex]
partial equation is y = [tex]\frac{4}{3}[/tex] x + c
to find c substitute any of the 3 points into the partial equation
using (3, 6 ), then
6 = 8 + c ⇒ = 6 - 8 = - 2 ⇒ (0, - 2 )← y-intercept
y= [tex]\frac{4}{3}[/tex] x - 2 ← equation of line
To find the x-intercept, let y = 0, in the equation and solve for x
[tex]\frac{4}{3}[/tex] - 2 = 0 ( add 2 to both sides )
[tex]\frac{4}{3}[/tex] x = 2 ( multiply by 3 and divide by 4 )
x = [tex]\frac{3}{2}[/tex] ⇒ ( [tex]\frac{3}{2}[/tex], 0) ← x-intercept
