To convert the equation 5x + 2y = 3 into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, we need to isolate y on one side of the equation.
Here’s how to do it:
- Start with the original equation:
- Subtract 5x from both sides to begin isolating y:
- Now, divide every term by 2 to solve for y:
5x + 2y = 3
2y = -5x + 3
y = - rac{5}{2}x + rac{3}{2}
Now, we have the equation in slope-intercept form:
y = - rac{5}{2}x + rac{3}{2}
This shows that the slope (m) is -5/2 and the y-intercept (b) is 3/2. Therefore, the slope-intercept form of the equation 5x + 2y = 3 is y = - rac{5}{2}x + rac{3}{2}.