The slope-intercept form of a linear equation is given by the equation y = mx + b, where m represents the slope of the line, and b represents the y-intercept.
To convert the equation 2x + 8y = 32 into slope-intercept form, we need to isolate y on one side of the equation. Let’s go through the steps:
- Start with the original equation:
2x + 8y = 32
- Subtract 2x from both sides:
8y = -2x + 32
- Now, divide every term by 8 to solve for y:
y = - rac{2}{8}x + rac{32}{8}
- Simplify the fractions:
y = - rac{1}{4}x + 4
Thus, the slope-intercept form of the equation 2x + 8y = 32 is y = - rac{1}{4}x + 4.
From this form, we see that the slope m is - rac{1}{4} and the y-intercept b is 4. This means the line slopes downward to the right and crosses the y-axis at the point (0, 4).