Originally Posted by

**twohundredping**
18. Answered in your other thread

19.

(a) We can put the equation in slope intercept form where it is easy to see the slope and y-intercept.

Slope intercept form: y = m*x + b, where m is the slope and b is the y-intercept

2y + x = 6

2y = 6 - x

y = 3 - x/2 = -x/2 + 3 = -1/2 * x + 3

Therefore, the slope is -1/2 and the y-intercept is 3.

(b) Here they gave us one point (3, 2) and told us the y-intercept is 1. There are two approaches we can use to solve the problem from here.

Approach 1:

y = m*x + b

Since the y-intercept is 1, b = 1

y = m*x + 1

Now we can plug in the point (3,2) for x and y.

2 = m * 3 + 1

1 = 3m

m = 1/3

So the equation of the line is:

y = 1/3 * x + 1

We can plug in the point (3,2) to verify that we did everything correctly

Approach 2:

Since the y-intercept is 1, we know that b = 1 and that the point (0, 1) is on the line.

Now we can find the slope between (3,2) and (0,1) as:

(2 - 1) / (3 - 0) = 1/3

Now we can give the equation of the line as:

y = 1/3 * x + 1

We can plug in the point (3,2) to verify that we did everything correctly

(c) y = 3 * x + b

Now plug in the point they give you.

1 = 3 * 2 + b

-5 = b

So y = 3 * x - 5 is the equation of the line.

(d) The x-intercept is the point where y = 0.

x-intercept of (a): 2x + 0 = 6

x = 3 is the x-intercept

x-intercept of (b): 0 = 1/3 * x + 1

-1 = 1/3 * X __WHat did you do here to get -3?__

x = -3 is the x-intercept __Can you help me understand how you got this -3? __

x-intercept of (x): 0 = 3 * x - 5

5 = 3 * x

x = 5/3 is the x-intercept