The equation $4x + 16y = 16$ is a linear equation in two variables, $x$ and $y$. To simplify it and express $y$ in terms of $x$, we can rewrite it in slope-intercept form, $y = mx + b$.

Solution Steps

1. Start with the equation: $4x + 16y = 16$

2. Move $4x$ to the other side by subtracting it from both sides: $16y = -4x + 16$

3. Divide every term by 16 to isolate $y$: $y = -\frac{4}{16}x + \frac{16}{16}$

4. Simplify the fractions: $y = -\frac{1}{4}x + 1$

Final Equation in Slope-Intercept Form

$y = -\frac{1}{4}x + 1$

This form shows that the slope of the line is $-\frac{1}{4}$ and the y-intercept is $1$.

Would you like more details, or do you have any questions?

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1. How would you solve this if asked for $x$ in terms of $y$?
2. What is the slope of this line, and what does it indicate about the line's direction?
3. How would you find the x-intercept of this line?
4. Can you convert this equation to standard form $Ax + By = C$ with integer values?
5. How would you graph this line on a coordinate plane?

Tip: To find the x-intercept, set $y = 0$ and solve for $x$.