10. Solve for y: 4x+3y=18 Show-your work. What form is the current linear equativ written in: __ )

<br /><br />The given equation is $4x+3y=18$. This is in the standard form of a linear equation, which is $Ax + By = C$, where A, B, and C are constants.<br /><br />To solve for y, we need to isolate y on one side of the equation. We can do this by subtracting $4x$ from both sides of the equation.<br /><br />\[\begin{aligned} <br />4x + 3y & = 18 \\<br />-4x + 4x + 3y & = -4x + 18 \\<br />3y & = -4x + 18<br />\end{aligned}\]<br /><br />Next, we divide both sides of the equation by 3 to solve for y.<br /><br />\[\begin{aligned} <br />3y & = -4x + 18 \\<br />\frac{3y}{3} & = \frac{-4x + 18}{3} \\<br />y & = -\frac{4}{3}x + 6<br />\end{aligned}\]<br /><br />So, the solution for y in terms of x is $y = -\frac{4}{3}x + 6$. This is the slope-intercept form of a linear equation, which is $y = mx + b$, where m is the slope and b is the y-intercept. In this case, the slope is $-\frac{4}{3}$ and the y-intercept is 6.