Question

fill in the missing numbers to complete the linear equation that gives the rule for this table. 8th grade

Answer 1

to find the slope of any straight line, we can simply use two points on that line

`\bf \begin{array}cc \cline{1-2} x&y\\ \cline{1-2} 3&-12\\ \underline{4}&\underline{-16}\\ 5&-20\\ \underline{6}&\underline{-24} &\\ \cline{1-2} \end{array}~\hspace{5em} (\stackrel{x_1}{4}~,~\stackrel{y_1}{-16})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{-24}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-24-(-16)}{6-4}\implies \cfrac{-24+16}{6-4}`

`\bf \cfrac{-8}{2}\implies -4 \\\\\\ \begin{array}ll \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-16)=-4(x-4) \\\\\\ y+16=-4x+16\implies y=-4x+0`