Question

#4 home do I find which one it is?

Answer 1

$\bf \begin{array}{lllll} solutions&graphs&slopes\\ ----&----&----\\ \textit{exactly one}& \begin{array}{llll} \textit{the two lines intersect}\\ \textit{at one point} \end{array}&\textit{different slopes}\\\\ infinitely\quad many& \begin{array}{llll} \textit{the two lines coincide}\\ \textit{one is right on top}\\ \textit{ of the other} \end{array}& \begin{array}{llll} \textit{equal slopes}\\ \textit{equal y-intercepts} \end{array} \end{array}$

$\bf \textit{no solution}\qquad\quad &\textit{lines are parallel} \qquad & \begin{array}{llll} \textit{equal slopes}\\ \textit{different y-intercepts} \end{array} \end{array}$

for example, let's look at the first set

y+3x =5   or  y = -3x+ 5
and               y = -3x + 2
                    y =  m  + b

the slopes are equal, the y-intercepts differ
that means, they're just parallel lines, no solution