Question

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?

Answer 1

Answer:

$The\ two\ lines\ intersect\ at\ (4,7).$

Step-by-step explanation:

Slope$(m)$ of line passing through $(x_1,y_1)\ and\ (x_2,y_2)$ is given by $\frac{y_2-y_1}{x_2-x_1}$.

Slope intercept form of line is given by: $y=mx+b$

First Line:

Let first line is $y=m_1x+b_1$

$m_1=\frac{8-4}{5-1}=\frac{4}{4}=1\\\\Line:\ y=x+b_1\\\\It\ passes\ through\ (1,4)\\\\4=1+b_1\Rightarrow\ b_1=3\\\\First\ line\ y=x+3$

Second Line:

Let second line is $y=m_2x+b_2$

$m_2=\frac{4-10}{6-2}=\frac{-6}{4}=-\frac{3}{2}\\\\Line:\ y=-\frac{3}{2}x+b_2\\\\It\ passes\ through\ (2,10)\\\\10=-3+b_2\Rightarrow\ b_2=13\\\\Second\ line\ y=-\frac{3}{2}x+13$

Point of Intersection of Two Lines:

$Solve\\\\y=x+3\\\\y=-\frac{3}{2}x+13\\\\\\x+3=-\frac{3}{2}x+13\\\\x+\frac{3}{2}=13-3\\\\\frac{5}{2}x=10\\\\x=\frac{2}{5}\times 10\\\\x=4\\\\Since\ y=x+3\\\\y=4+3=7\\\\Point\ of\ intersection\ is\ (4,7)$

Answer 2

Answer:

4, 7

Step-by-step explanation:

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