Question

Identify the slope and y-intercept for the following line: 5x - 2y = 8

Tip: Graph or re-write as y = mx+b
1. m = -2/5, b = 4
2. m = 2/5, b = -4
3. m = 5/2, b = -4
4. m= -5/2, b = 4

Answer 1

The slope (m) of the line represented by the equation 5x - 2y = 8 is 5/2, and the y-intercept (b) is -4 when rearranged into the slope-intercept form, which is y = mx + b.

Step-by-step explanation:

The goal is to identify the slope and y-intercept of the line represented by the equation 5x - 2y = 8. To do this, we need to rearrange the equation into the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

First, solve for y:

1. Add 2y to both sides: 5x = 2y + 8
2. Subtract 8 from both sides: 5x - 8 = 2y
3. Divide every term by 2 to solve for y: y = (5/2)x - 4

From the final equation y = (5/2)x - 4, we can see that the slope m is 5/2 and the y-intercept b is -4. Therefore, the correct option is 3: m = 5/2, b = -4.