Determine the slope and y-intercepts

2x = 3y + 4

8x − 2y − 3 = 0

To find y-intercepts, let x = 0 and solve for Y.

1. 2x = 3y+4
2x-3y = 4
m = -A/B = -2/-3 = 2/3.

2*0-3y = 4
-3y = 4
Y = -4/3 = y-int.

2. 8x-2y-3 = 0
8x-2y = 3
Use same procedure as #1.

To determine the slope and y-intercept of an equation, we need to rearrange the equation into slope-intercept form, which is in the form y = mx + b, where m is the slope and b is the y-intercept.

Let's start with the first equation: 2x = 3y + 4.

Step 1: Isolate y on one side of the equation:
Divide both sides of the equation by 3 to obtain: (2/3)x = y + (4/3).

Step 2: Rearrange the equation to slope-intercept form:
Subtract (4/3) from both sides of the equation to get: y = (2/3)x - (4/3).

Now we can determine the slope and y-intercept from this equation.
The slope (m) is the coefficient of x, which is 2/3.
The y-intercept (b) is the constant term, which is -4/3.

Therefore, the slope of the equation 2x = 3y + 4 is 2/3, and the y-intercept is -4/3.

Let's move on to the second equation: 8x − 2y − 3 = 0.

Step 1: Rearrange the equation to slope-intercept form:
Add 3 to both sides of the equation to get: 8x - 2y = 3.
Subtract 8x from both sides to isolate -2y: -2y = -8x + 3.
Then divide all terms of the equation by -2: y = (8/2)x - (3/2).
Simplifying gives us: y = 4x - 3/2.

Now we can determine the slope and y-intercept.
The slope (m) is the coefficient of x, which is 4.
The y-intercept (b) is the constant term, which is -3/2.

Therefore, the slope of the equation 8x − 2y − 3 = 0 is 4, and the y-intercept is -3/2.