##### How many minutes does it take Arnob to catch up to Kathleen?

 Algebra Tutor: None Selected Time limit: 1 Day

Jun 24th, 2015

We can use the point slope form of a line to find the equation of the 2 linear functions.

(-3, -10) and (0, 2) are points on the first line.

Slope of first line,

$\\ m=\frac{y_2-y_1}{x_2-x_1}\\ \\ m=\frac{2-(-10)}{0-(-3)}\\ \\ m=\frac{2+10}{0+3}\\ \\ m=\frac{12}{3}\\ \\ m=4$

Point slope form of equation of a line is

$y-y_0=m(x-x_0)\\ \\$

where m is the slope of the line

and $(x_0,y_0)$ is a point on the line.

Take $(x_0,y_0)$ = (0, 2)

So, equation of the first line is

$\\ y-2=4(x-0)\\ \\ y-2=4x\\ \\ y=4x+2---(1)$

(0, -12) and (3, -3) are points on the first line.

Slope of second line,

$\\ m=\frac{y_2-y_1}{x_2-x_1}\\ \\ m=\frac{-3-(-12)}{3-0}\\ \\ m=\frac{-3+12}{3}\\ \\ m=\frac{9}{3}\\ \\ m=3$

Take $(x_0,y_0)$ = (0, -12)

So, equation of second line is

$\\ y-(-12)=3(x-0)\\ \\ y+12=3x\\ \\ y=3x-12---(2)$

Substitute y from equation (1) into equation (2)

4x + 2 = 3x - 12

4x - 3x = -12 - 2

x = -14

Substitute value of x in equation (1)

y = 4*(-14) + 2

y = -56 + 2

y = -54

So, solution is (-14, -54) .

Jun 24th, 2015

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Jun 24th, 2015
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Jun 24th, 2015
Dec 7th, 2016
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