To rewrite the equation 5x + 2y = 10 in the slope-intercept form, which is y = mx + b, we need to solve for y.
- Start with the original equation:
5x + 2y = 10 - Isolate the term with y:
Subtract 5x from both sides:
2y = 10 – 5x - Now, divide every term by 2:
y = (10 – 5x) / 2 - Simplify the right side:
y = 5 – (5/2)x
Now we can express it in the form of y = mx + b. In this case:
- m (slope) = -5/2
- b (y-intercept) = 5
So, the final equation in slope-intercept form is:
y = -2.5x + 5
This means that for every 1 unit increase in x, y will decrease by 2.5 units, and the line crosses the y-axis at 5.