Pre Alg (Check my work?)
1.) In which Quadrant is the point (x,y) located if x is negative and y is positive? II III IV (MY ANSWER) I 2.) Point A(5,-10) is reflected over the Y axis. Write the coordinates of A'. (-8,-10) (8,10) (8,-10) MY CHOICE (-8,10)
3.Graph the points A(–5, 0 ), B(–4, 3), and C(0, –4) on the same coordinate plane. 2. Without graphing, identify the quadrant in which the point (x, y) lies if x < 0 and y < 0. (1 point) 3.Determine which ordered pair is a
line segment ab is the diameter of circle O whose center has coordinates (6,8) . what are the coordinates of point b if the coordinates of point a are (4,2)
The endpoints of AB are A(2, 3) and B(8, 1). The perpendicular bisector of AB is CD , and point C lies on AB. The length of CD is √10 units. The coordinates of point C are_____ . The slope of CD is _____ . The possible
Properties of a straight line
Step 1 :
Equation of a Straight Line
1.1 Solve 2x-3y-21 = 0
Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
In this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 2x-3y-21 = 0 and calculate its properties
Graph of a Straight Line :
Calculate the Y-Intercept :
Notice that when x = 0 the value of y is 7/-1 so this line "cuts" the y axis at y=-7.00000y-intercept = 21/-3 = 7/-1 = -7.00000
Calculate the X-Intercept :
When y = 0 the value of x is 21/2 Our line therefore "cuts" the x axis at x=10.50000x-intercept = 21/2 = 10.50000
Calculate the Slope :
Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -7.000 and for x=2.000, the value of y is -5.667. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -5.667 - (-7.000) = 1.333 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)Slope = 1.333/2.000 = 0.667
Geometric figure: Straight Line
- Slope = 1.333/2.000 = 0.667
- x-intercept = 21/2 = 10.50000
- y-intercept = 21/-3 = 7/-1 = -7.00000
Here we will show you how to calculate and provide solutions to math problems related to 2x + 3y = 21.
We will start by calculating and showing you the solution for the x-intercept and y-intercept of 2x + 3y = 21.
Then, we will show you how to get the graph plot coordinates for 2x + 3y = 21 so we can illustrate it on a graph.
Finally, we will solve 2x + 3y = 21 for x and also for y, then calculate and show you the solution for the slope of 2x + 3y = 21.
The x-intercept is where the graph crosses the x-axis. To find the x-intercept, we set y1=0 and then solve for x.
2x + 3y = 21
2x + 3(0) = 21
x1 = 10.5 y1 = 0
The y-intercept is where the graph crosses the y-axis. To find the y-intercept, we set x2=0 and then solve for y.
2x + 3y = 21
2(0) + 3y = 21
y2 = 7 x2 = 0
Get Graph Plot Coordinates
Getting two graph points will allow you to make a straight line on a graph. The plot coordinate format is (x1,y1) and (x2,y2).
Thus, we use the x-intercept and y-intercept results above to get the graph plots for 2x + 3y = 21 as follows:
(x1,y1) and (x2,y2)
Solve for x
To solve for x, we solve the equation so the variable x is by itself on the left side:
2x + 3y = 21
x = 10.5 - 1.5y
Solve for y
To solve for y, we solve the equation so the variable y is by itself on the left side:
2x + 3y = 21
y = 7 - 0.667x
The slope of the line (m) is the steepness of the line. It is the change in the y coordinate divided by the corresponding change in the x coordinate. Simply plug in the coordinates from above and solve for m to get the slope for 2x + 3y = 21
m = (y2- y1)/(x2- x1)
m = (7 - 0)/(0 - 10.5)
m = -0.667
Ax + By = C Calculator
Now you know how to solve 2x + 3y = 21. Enter another math problem here:
2x + 3y = 22
Here is the next algebra problem on our list. Check it out!
Answers are rounded to the nearest thousandth if necessary. If you want exact answers instead of rounded answers, then keep the fraction answers when you solve the equations instead of converting them to decimal numbers like we did.
21 2x 3y
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