1. Write an equation in slope-intercept form for the line that passes through (3,5) and (-2,1).

2. Describe the system 6x-2y=10 and 9x-3y=8 as consistent and independent, consistent and dependent, or inconsistent. Explain

1. The slope-intercept form is

y = mx + b
Write these two equations that must be satisfied for the two points:
5 = 3m + b
1 = -2m + b
Subtract the second from the first:
4 = 5m m = 4/5
5 = 12/5 + b
b = 13/5 etc.

2. Multiply the first equation by 1.5 and get
9x - 3y = 15
This is inconsistent wth the second equation. They repreesnt two parallel lines. They cannot both be satisfied at any point in (x,y) space.

1. To write an equation in slope-intercept form, we need to use the formula: y = mx + b, where "m" represents the slope and "b" represents the y-intercept.

Step 1: Find the slope using the formula m = (y₂ - y₁) / (x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are the coordinates given in the problem.
Let's use the points (3,5) and (-2,1) to find the slope:
m = (1 - 5) / (-2 - 3) = -4 / -5 = 4/5

Step 2: Plug in the slope value (4/5) and one of the points (let's use (3,5)) into the slope-intercept form equation:
y = mx + b
5 = (4/5) * 3 + b

Step 3: Solve for "b" by substituting the given values into the equation and solving for "b":
5 = (4/5) * 3 + b
5 = 12/5 + b
b = 5 - 12/5
b = 25/5 - 12/5
b = 13/5

Therefore, the equation in slope-intercept form for the line passing through (3,5) and (-2,1) is:

y = (4/5)x + 13/5

2. To determine if the system of equations is consistent and independent, consistent and dependent, or inconsistent, we need to look at the solutions.

Let's solve the given system of equations:

6x - 2y = 10 ---> Equation 1
9x - 3y = 8 ---> Equation 2

We can observe that both equations have the same ratios of coefficients:

3 * (6x - 2y) = 3 * 10
2 * (9x - 3y) = 2 * 8

18x - 6y = 30 ---> Equation 3
18x - 6y = 16 ---> Equation 4

When we compare Equations 3 and 4, we can see that they are the same equation. This implies that the systems of equations are dependent since they represent the same line or set of lines.

Therefore, the system of equations 6x - 2y = 10 and 9x - 3y = 8 is consistent and dependent.