To write the equation in slope-intercept form, we need to rearrange the given equation, which is 3x + 10y = 7, into the form y = mx + b, where m represents the slope and b represents the y-intercept.
Here are the steps to convert the equation:
- Start with the original equation: 3x + 10y = 7.
- To isolate y, subtract 3x from both sides: 10y = 7 – 3x.
- Now, divide every term by 10 to solve for y: y = - rac{3}{10}x + rac{7}{10}.
This is now in slope-intercept form. From the equation y = - rac{3}{10}x + rac{7}{10}, we can identify:
- Slope (m): - rac{3}{10}
- Y-Intercept (b): rac{7}{10}
In summary, the slope of the equation is - rac{3}{10} and the y-intercept is rac{7}{10}. This means that for every 10 units you move horizontally, the line goes down 3 units.