Respuesta :
Answer:
The equation [tex]y=-\frac{2}{3}x+2[/tex]
Step-by-step explanation:
Equations of the form [tex]ax+by=c[/tex] are known as Standard Form for a linear equation in two variables, x and y, in the case of your equation [tex]2x+3y=6[/tex] where a = 2, b = 3 and c = 6.
Equations of the form [tex]y = -\frac{ax}{b}+\frac{c}{b}[/tex] are known as Slope-Intercept form. This is called in this way because [tex]-\frac{a}{b}[/tex] is equal to the slope of the line, and [tex]\frac{c}{b}[/tex] is the value of y when x = 0, which makes it the y-intercept.
To convert from standard form [tex]2x+3y=6[/tex] to slope-intercept form [tex]y = -\frac{ax}{b}+\frac{c}{b}[/tex], we need to follow these steps:
- Subtract 2x from both sides [tex]2x+3y-2x=6-2x[/tex]
- Simplify [tex]3y=6-2x[/tex]
- Divide both sides by 3 [tex]\frac{3y}{3} =\frac{6}{3}-\frac{2x}{3}[/tex]
- Simplify [tex]y = 2-\frac{2x}{3} = -\frac{2x}{3} + 2[/tex]
