To find the value of a, we'll follow these steps:
1. Rewrite the equation in slope-intercept form (y = mx + b), where m is the slope.
2. Compare the coefficient of x in the slope-intercept form to the given slope to determine a.
Rewriting in slope-intercept form:
- 2x - ay + 5 = 0
- -ay = -2x - 5
- y = (2/a)x + 5/a (dividing both sides by -a)
Comparing slopes:
- The slope in the slope-intercept form is 2/a.
- The given slope is 3/2.
- Therefore, 2/a = 3/2.
Solving for a:
- Cross-multiplying gives 4 = 3a.
- Dividing both sides by 3 yields a = 4/3.
- Therefore, the value of a is 4/3.
