To find the slope and y-intercept of the line given by the equation 18x + 4y = 112, we need to rearrange the equation into the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
Here are the steps:
- Start with the original equation:
- Isolate 4y on one side by subtracting 18x from both sides:
- Next, divide every term by 4 to solve for y:
- Simplifying the fractions gives:
18x + 4y = 112
4y = -18x + 112
y = - rac{18}{4}x + rac{112}{4}
y = -4.5x + 28
From the equation y = -4.5x + 28, we can identify the slope and y-intercept:
- Slope (m): -4.5
- Y-Intercept (b): 28
In summary, the slope of the line is -4.5, and the y-intercept is 28. This means that for every unit increase in x, the value of y decreases by 4.5, and the line crosses the y-axis at the point (0, 28).