Hello!
First, let's remember how to write the equation in the slope-intercept form:
[tex]\mathrm{y=mx+b}[/tex]
• m ,= slope (angular coefficient)
,
• b ,= y-intercept (linear coefficient)
Knowing it, let's write each alternative in the slope-intercept form:
a.
• m = -2/3
,
• b = -5
[tex]y=-\frac{2}{3}x-5[/tex]
b.
m = 3
b = 0
[tex]\begin{gathered} y=3x+0 \\ y=3x \end{gathered}[/tex]
c.
m = 7
b = -3
[tex]y=7x-3[/tex]
d.
• m = 0
,
• b = 12
[tex]\begin{gathered} y=0x+12 \\ y=12 \end{gathered}[/tex]
To write the equation in the standard form, we just need to follow one step:
We will isolate the number without variables on one side of the equation. Look:
a. 2x +3y = -15
[tex]\begin{gathered} y=-\frac{2}{3}x-5 \\ \\ y+\frac{2}{3}x=-5\text{ let's remove the fraction by multiplying both sides by 3} \\ \\ (3)\cdot y+\frac{2}{3}x=-5\cdot(3)\text{ } \\ \\ 2x+3y=-15 \end{gathered}[/tex]
b. 3x -y =0
[tex]\begin{gathered} y=3x \\ 3x-y=0 \end{gathered}[/tex]
c. -7x +y = -3
[tex]\begin{gathered} y=7x-3 \\ y-7x=-3 \\ -7x+y=-3 \end{gathered}[/tex]
d. y = 12
[tex]y=12[/tex]
