Hello!
First, we have to remember that the equation of the line has the form:
y = mx + b
• m, = slope
,
• b, = y-intersection
Knowing it, we can solve this exercise:
1st equation: 5x -6y = 30
Let's isolate y:
[tex]\begin{gathered} 5x-6y=30 \\ -6y=30-5x \\ -y=\frac{30}{6}-\frac{5x}{6} \\ (-1)\cdot-y=5-\frac{5x}{6}\cdot(-1) \\ y=\frac{5x}{6}-5 \end{gathered}[/tex]
Slope: 5/6
Y-intercept: (0, -5)
2nd equation: y = 5 -6x
Slope: -6x
Y-intercept: (0, 5)
3rd equation: y = 5/6x +1
Slope: 5/6
Y-intercept: (0, 1)
4th equation: 5x -6y = 6
Let's isolate y:
[tex]\begin{gathered} 5x-6y=6 \\ -6y=6-5x \\ -y=\frac{6}{6}-\frac{5x}{6} \\ (-1)\cdot-y=1-\frac{5x}{6}\cdot(-1) \\ y=\frac{5x}{6}-1 \end{gathered}[/tex]
Slope: 5/6
Y-intercept: (0, -1)
5th equation: 5x + 6y = 6
Let's isolate y:
[tex]\begin{gathered} 5x+6y=6 \\ 6y=6-5x \\ y=\frac{6}{6}-\frac{5x}{6} \\ y=-\frac{5x}{6}+1 \end{gathered}[/tex]
Slope: -5/6
Y-intercept: (0, 1)
6th equation: 6x +y = 12
[tex]y=-6x+12[/tex]
Slope: -6
Y-intercept: (0, 12)
Look at your answers below:
