Question

Consider the following equations:Equation A: 2x – 3y = 18Equation B: 40 - 6y=-6Which of the statements below are true?The slopes and y-intercepts of both lines are different.The slopes and y-intercepts of both lines are the same.The slopes of both lines are the same and the y-intercepts are different.The slopes of both lines are different and the y-intercepts are the same.

Answer 1

`\begin{gathered} we\text{ will express y in terms of x foir both equation} \\ A\colon-3y=18-2x \\ A\colon3y=2x-18 \\ A\colon y=(2)/(3)x-6 \\ \\ \\ B\colon4x-6y=-6 \\ B\colon-6y=-6-4x \\ B\colon6y=4x+6 \\ B\colon y=(4)/(6)x+1 \\ B\colon y=(2)/(3)x+1_{} \\ \\ \text{ thus the slopes of both lines are the same and the y-intercepts are different!} \end{gathered}`

`\begin{gathered} we\text{ will express y in terms of x foir both equation} \\ A\colon-3y=18-2x \\ A\colon3y=2x-18 \\ A\colon y=(2)/(3)x-6 \\ \\ \\ B\colon4x-6y=-6 \\ B\colon-6y=-6-4x \\ B\colon6y=4x+6 \\ B\colon y=(4)/(6)x+1 \\ B\colon y=(2)/(3)x+1_{} \\ \\ \text{ thus the slopes of both lines are the same and the y-intercepts are different!} \end{gathered}`