Chapter 5 - Coordinate Plane

Question 1

What is the slope of the line?

Answer 1

The slope of a line is defined as “rise over run”. How much the line RISES vertically divided by how much the line RUNS horizontally.

Slope= rise/run = change in Y/change in X

Question 2

What are the 4 types of slopes?

Answer 2

1) Positive slope - rises upward from left to right.
2) Negative slope- falls downward from left to right.
3) Zero slope - horizontal line since there is no rise over run.
4) Vertical slope - undefined slope

Question 3

What are the intercepts of a line?

Answer 3

A point where a line intersects a coordinate axis is called an intercept.

The X- intercept is the point on the line at which y=0.

The Y- intercept is the point on the line at which x=0.

To find x- intercept, plug is 0 for y. To find y- intercept, plug in 0 for x.

Question 4

What is the equation of a line?

Answer 4

y=mx+b. This is a linear equation

m= slope

b= y intercept

Question 5

What is the equation for horizontal and vertical lines?

Answer 5

Horizontal lines are expressed in the form: y= some number. All points on a horizontal line have the same y-coordinate. This is why the equation of a horizontal line is defined only by y.

Vertical lines are expressed in the form: x= some number. All points on a vertical line have the same x-coordinate. This is why the equation of a vertical line is defined only by x.

Question 6

List the step by step: equation of line given 2 points to a Line

Answer 6

Q: Find the equation of the line containing the points (5,-2) and (3,4)

1) Find the slope of the line by calculating the rise over the run.

rise/run= change in y/change in x = -2-4/5-3= -6/2= -3

The slope of the line is -3. It is imp to keep the x and y coordinate in the same order bc the signs are imp

2) Plug the slope in for m in the slope-intercept equation.

y=-3x+b

3) Solve for b, the y intercept by plugging the coordinates of one point into the equation. Either point’s coordinate will work.

Plugging the point (3,4) into the equation (3 for x and 4 for y):

4= - 3(3)+b

4= - 9+b

b= 13 : The y-intercept of the line is 13.

4) Write the equation in the form y=mx+b

y= - 3x+13 : This is the equation of the line.

Question 7

How can you calculate the distance between 2 points using the points (1,3) and (7,-5)?

Answer 7

The distance between any two points in the coordinate plane can be calculated by using the Pythagorean Theorem.

1) Draw a right triangle by connecting the points.
2) Find the lengths of the two legs of the triangle by calculating the rise and the run.

The y-coordinate changes from 3 to 5, a diff of 8 on the vertical leg.

The x-coordinate changes from 1 to 7, a diff of 6 on the horizontal leg.

3) Using Pyth Therom, calculate 3rd side as 10. This is a variation of the 3-4-5 triangle.

Question 8

In which direction to the Quadrants in the coordinate plane work?

Answer 8

Counterclockwise

         II              I

         III             IV

Question 9

Which quadrant does the line 2x+y=5 pass through?

Answer 9

1) Rewrite the line in the form y=mx+b

2x+y=5

y= - 2x+5 = slope is -2 and y intercept is 5.

2) So sketch the line with y intercept of (0,5). The slope is -2 so the line slopes downward steeply to the right from the y intercept. This approach wont exactly tell you where the line intersects the x axis but you can see that the line will pass through quad I, II, IV.
3) Alternatively, you can find two points on the line by setting x and y equal to zero in the ORIGINAL equation.

x=0 y=0

2x+y=5 2x+y=5

2(0)+y=5 2x+0=5

y=5 x= 2.5

So the line passes through y coordinates of (0,5) and x coordinates of (2.5, 0) which is quadrant I, II, IV