what are the plots like (x,y) so i can graph thesse??? 10 points rewarded?

Question

y= -2/3x +4 by graphing 3 points.

y= x - 3 by graphing 3 points.

3x - 2y = 6 by graphing the x and y intercepts.

-x + 3y = -9 by graphing the x and y intercepts.

4x - 3y = 6 by the slope intercept method.

3x + 5y = 12 by the slope intercept method.

Answer 1

They are all equations of lines.

y = -2/3x + 4. I choose x=0, x=3. x=6
x=0: y = (-2/3)*0 + 4 = 4 so point is (0,4)
x=3: y = (-2/3)*3 + 4 = 2 so point is (3,2)
x=6: y = (-2/3)*6 + 4 = 0 so point is (6,0)

Plot these three points and draw the line through them (actually, two points are sufficient, but a third point will confirm.)

The next one is very similar. It's yours.


3x - 2y = 6 using x and y intercepts

The x intercept (where the line intersects the x axis) is found by setting y=0:

3x - 2*0 = 6
3x=6
x=2 The x intercept is (2,0)

The y intercept (where the line intersects the y axis) is found by setting x=0:

3*0 - 2y = 6
-2y = 6
y= - 3. The y intercept is (0,-3)

Plot these two points and draw the line through them.

The next one is done similarly. I leave it to you.


4x - 3y = 6 by slope intercept method.
Slope-intercept form of the equation of a line is y = mx + b where m is the slope and b is the y intercept.

4x - 3y = 6
-3y = 6 - 4x
y = (4/3)x - 2

Slope is 4/3, y intercept is -2. So the point (0,-2) is on the line. One way to use the slope to draw the line is to recall that slope=rise/run, so starting from the y-intercept draw a vertical line segment, 4 units in length, above the y-intercept; then from the end of that line segment draw a horizontal line segment, 3 units in length, extending to the right. The endpoint of that horizontal line segment is another point on the graph of the line. This point will have the coordinates (0+3, -2+4) = (3,2). It's a good idea to confirm that this point does satisfy the equation of the line: 4*3 - 3*2 = 6 check!

The last equation is handled in much the same way. Note: its slope is negative, so draw the vertical line segment down from the y intercept, and the horizontal segment to the right.