Question

Which of the following equations is 2x + 3y = 6 written in slope-intercept form.

Answer 1

Y=(2/3)×+2 yuhhuhyhhy

Answer 2

Answer:

The equation $y=-\frac{2}{3}x+2$

Step-by-step explanation:

Equations of the form $ax+by=c$ are known as Standard Form for a linear equation in two variables, x and y, in the case of your equation  $2x+3y=6$ where a = 2, b = 3 and c = 6.

Equations of the form $y = -\frac{ax}{b}+\frac{c}{b}$ are known as Slope-Intercept form. This is called in this way because $-\frac{a}{b}$ is equal to the slope of the line, and $\frac{c}{b}$ is the value of y when x = 0, which makes it the y-intercept.

To convert from standard form $2x+3y=6$ to slope-intercept form $y = -\frac{ax}{b}+\frac{c}{b}$, we need to follow these steps:

1. Subtract 2x from both sides $2x+3y-2x=6-2x$
2. Simplify $3y=6-2x$
3. Divide both sides by 3 $\frac{3y}{3} =\frac{6}{3}-\frac{2x}{3}$
4. Simplify $y = 2-\frac{2x}{3} = -\frac{2x}{3} + 2$