Final answer:
To find the slope of the line from the equation 3x + 5y = 2x + 3y, rearrange it to the form y = mx + b. The resulting slope is -1/2, indicating that for each unit increase in x, y decreases by 1/2 unit.
Step-by-step explanation:
To find the slope of the line represented by the equation 3x + 5y = 2x + 3y, you first simplify the equation to its slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept. Let's rearrange the given equation:
- Subtract 2x from both sides to get: x + 5y = 3y.
- Subtract 5y from both sides to get x = -2y.
- Divide both sides by -2 to isolate y and get y = -1/2 x. Now we can see that the slope (m) is -1/2.
The slope of the line is the rate at which y is changing with respect to x. In reference to Figure A1, if we had an equation in the form y = mx + b, such as y = 9 + 3x, the slope here would be 3, which means for every 1 unit increase in x, y increases by 3 units. The slope is consistent along the entire length of a straight line.