Final answer:
To convert 2x-5y=10 into slope-intercept form, subtract 2x from both sides, then divide by -5, giving y = (2/5)x - 2, which shows a slope of 2/5 and a y-intercept of -2.
Step-by-step explanation:
The student is asking to convert the given linear equation 2x-5y=10 into slope-intercept form, which is given by y = mx + b, where m represents the slope, and b is the y-intercept.
To convert 2x-5y=10 into slope-intercept form, follow these steps:
Subtract 2x from both sides of the equation: -5y = -2x + 10.
Divide each term by -5 to solve for y: y = (2/5)x - 2.
Now, the equation is in slope-intercept form y = (2/5)x - 2, where the slope (m) is 2/5 and the y-intercept (b) is -2.
The slope of 2/5 means there is a rise of 2 units on the vertical axis for every increase of 5 units on the horizontal axis. The y-intercept of -2 indicates that the line crosses the y-axis at the point (0, -2).