To convert the equation 3x + 10y = 7 into slope-intercept form, which is defined as y = mx + b (where m is the slope and b is the y-intercept), follow these steps:
- Start with the original equation: 3x + 10y = 7.
- Subtract 3x from both sides to isolate the term with y: 10y = -3x + 7.
- Next, divide every term by 10 to solve for y: y = -\frac{3}{10}x + \frac{7}{10}.
Now, in the format y = mx + b, you can see that:
- The slope m is -\frac{3}{10}.
- The y-intercept b is \frac{7}{10} (which means the line crosses the y-axis at (0, \frac{7}{10})).
Thus, the slope-intercept form of the equation is y = -\frac{3}{10}x + \frac{7}{10}, with a slope of -\frac{3}{10} and a y-intercept of \frac{7}{10}.