Final answer:
The given equations 3x + 5y = 12 and 5x – 4y = 6 have been rewritten in slope-intercept form as y = (-3/5)x + 12/5 and y = (5/4)x - 3/2, respectively, showing their slopes and y-intercepts.
Step-by-step explanation:
To rewrite the equation 3x + 5y = 12 in slope-intercept form, we need to solve for y to get it into the form y = mx + b, where m represents the slope and b represents the y-intercept. Here's the process:
- 3x + 5y = 12
- Subtract 3x from both sides: 5y = -3x + 12
- Divide every term by 5: y = (-3/5)x + 12/5
Now, the equation is in slope-intercept form with a slope of -3/5 and a y-intercept of 12/5.
Next, for the equation 5x – 4y = 6:
- 5x - 4y = 6
- Subtract 5x from both sides: -4y = -5x + 6
- Divide every term by -4: y = (5/4)x - 6/4
- Simplify the y-intercept: y = (5/4)x - 3/2
Now, the equation is in slope-intercept form with a slope of 5/4 and a y-intercept of -3/2.