A line passes through the points (1, 4) and (5,8). A second line passes through the points (2, 10) and (6, 4). At what point do the two lines intersect? ​

(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 =

with (x₁, y₁ ) = (1, 4) and (x₂, y₂ ) = (5, 8)

m = = = 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 = = = -

y = - x + c

Using (2, 10 ) to find c

10 = - 3 + c ⇒ c = 10 + 3 = 13

y = - x + 13 → (2)

Equate the right sides of (1) and (2)

x + 3 = - 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 )

isi

step-by-step explanation:

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