Question

Write a linear equation that contains the ordered pair shown in the table below:

Answer 1

Answer:

$y=2x-4$

Step-by-step explanation:

Let the equation of line is $y=mx+b$, where $m$ is the slope of the line.

It passes through $(-5,-14),(-2,-8)\ and\ (1,-2)$.

(Slope of the line joining $(x_1,y_1)\ and\ (x_2,y_2)=\frac{y_2-y_1}{x_2-x_1}$)

Hence slope of the given line

$m=\frac{-8(-14)}{-2-(-5)}=\frac{-8+14}{-2+5}=\frac{6}{3}=2$

Equation of line is: $y=2x+b$

The line passes through $(1,-2)$

$-2=2\times 1+b\\b=-2-2\\b=-4$

Check if $(-5,-14)$ is on the line $y=2x-4$

$L.H.S.=-14\\R.H.S.=2\times (-5)-4=-10-4=-14\\L.H.S.=R.H.S.$

Hence line passes through $(5,-14)$.

Check if $(-2,-8)$ is on the line $y=2x-4$

$L.H.S.=-8\\R.H.S.=2\times (-2)-4=-4-4=-8\\L.H.S.=R.H.S.$

Hence line passes through $(-2,-8)$.