Help!! can someone help me w/my algebra -i keep getting different answers every time!!!***?

Question

Problem #1-find the equation of (0,-3), (3,2),(6,7) and this one is making me nuts too!!
Problem #2-Graph y<-2/3rds x +4 or explain coordinants and if greater or less than or equal too-have to say yes or no-but i'm insane from these problems....thanks soo much...

Answer 1

Question 1
Gradient m = (7 - 2) / (6 - 3) = 5 / 3

Check
Gradient m = (2 + 3) / (3 - 0) = 5 / 3

Use any point to find equation:-
Point (3,2)
y - 2 = (5/3) (x - 3)
y - 2 = (5/3) x - 5
y = (5/3) x - 5 + 2
y = (5/3) x - 3

Question 2
Consider the line:-
y = (- 2/3) x + 4
To draw a line , require any two points on the line:-
Let points be (0 , 4) and (6 , 0)
Now draw a DOTTED line thro` these points.
Required region y < (-2/3)x + 4 is then the SHADED region that lies BELOW the dotted line.

Answer 2

Problem 1:

Slope-intercept form of a line: y = mx + b

m = slope, b = y-intercept

Use the first point listed (0, -3) to get the value of b:

-3 = m * (0) + b -------------> b = -3

Use either of the other two points to solve for the slope m:

m = (y - b)/x = (2 - (-3))/3 = (7 - (-3))/6 = 5/3

The equation for the line is:

y = (5/3)x - 3


Problem 2:

To visualize the line, plot these 7 points:

(-6, 8), (-3, 6), (-1.5, 5), (0, 4), (1.5, 3), (3, 2), (6, 0)

Once you plot the points, you'll see that the line's negative slope makes it angle downward to the right as x increases, passing through the y-axis at 4 (0,4) and the x-axis at 6 (6,0). If y were equal to the expression on the right side of the equation, each and every point on the line itself would be a valid solution, but since the "<" sign appears there instead, it means that ONLY the points below the line (i.e to the LEFT of it) are solutions.

Hope this helps