Question

These tables of ordered pairs represent some points on the graphs of lines s and t.

Which system of equations is represented by lines s and t?


5x−2y=−157x+4y=20


3x+5y=−185x−9y=25


x+4y=−89x−y=21


2x−y=−142x+y=6

Answer 1

The equation of line S is y = 2x + 14 while that of line T is y = -2x + 6.

A linear equation is in the form:

y = mx + b;

where y, x are variables, m is the slope of the line and b is the y intercept.

For line s, using the points: (-5, 4) and (4, 22). Hence:

$y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-4=\frac{22-4}{4-(-5)} (x-(-5))\\\\y-4=2(x+5)\\\\ y=2x+14$

Line T passes through the points (-4, 14) and (5, -4). Hence:

$y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-14=\frac{-4-14}{5-(-4)} (x-(-4))\\\\y-14=-2(x+4)\\\\ y=-2x+6$

Hence the equation of line S is y = 2x + 14 while that of line T is y = -2x + 6.

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