Answer:
(4, 7 )
Step-by-step explanation:
The first step is to obtain the equations of the lines and then solve simultaneously.
The equation of a line in slope0 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 ) = (1, 4) and (x₂, y₂ ) = (5, 8)
m = [tex]\frac{8-4}{5-1}[/tex] = [tex]\frac{4}{4}[/tex] = 1 then
y = x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (1, 4 ) , then
4 = 1 + c ⇒ c = 4 - 1 = 3
y = x + 3 → (1)
Repeat for points on line 2 (2, 10) and (6, 4)
m = [tex]\frac{4-10}{6-2}[/tex] = [tex]\frac{-6}{4}[/tex] = - [tex]\frac{3}{2}[/tex]
y = - [tex]\frac{3}{2}[/tex] x + c
Using (2, 10 ) to find c
10 = - 3 + c ⇒ c = 10 + 3 = 13
y = - [tex]\frac{3}{2}[/tex] x + 13 → (2)
Equate the right sides of (1) and (2)
x + 3 = - [tex]\frac{3}{2}[/tex] x + 13 ( multiply through by 2 to clear the fraction )
2x + 6 = - 3x + 26 ( add 3x to both sides )
5x + 6 = 26 ( subtract 6 from both sides )
5x = 20 ( divide both sides by 5 )
x = 4
Substitute x = 4 into (1) for corresponding value of y
y = 4 + 3 = 7
point of intersection = (4, 7 )
