Question

(Crys) Im in 11 grade and in applied geometry I need help crys and how do you show

Answer 1

Answer:

1. -2/3        3. -5/4         5. 3/2          FOR THE REST OF THE PARTS LOOK THROUGH THE EXPLANATIONS

Step-by-step explanation:

Before I start the workings, I'll give a little explanation on this topic.

So, the equation of a straight line is

y = mx + c

where x and y are any coordinates of any point on the line.

m is the gradient or slope

m can be calculated using 2 formulas,

formula 1: Rise/Run

where rise is the how much a graph goes upwards or downwards, if its upwards use positive integer and if its downwards use negative integer.

Run is how much a graph moves to the right or to the left, if it moves to the right is is positive, if it moves to the left it is negative.

Formula 2: (y2-y1)/(x2-x1)

the values of these are taken through any 2 coordinates on the line.

and c is the y-intercept(the point where the line crosses the y-axis.

MOVING TO ANSWERING NOW

1. Dotted points on the line are (1,0) and (4,-2)

Formula of slope,

U can use any of the 2 formulas given above

I'll show both for this question

m = (y2-y1)/(x2-x1) = (-2-0)/(4-1) = -2/3

OR

m = rise/run = where rise is -2 and run is 3 so -2/3

2. TRY DOING THIS ONE YOURSELF

For the next part I'll do 3 and 5 for your understanding, try doing 2 and 4 on your own to understand.

3. Coordinates given (13,1) and (1,16)

m = (y2-y1)/(x2-x1) = (16-1)/(1-13) = 15/-12  simplify this and it becomes -5/4

5.  (-8,-14) and (-10,-17)

m =  (y2-y1)/(x2-x1) = (-17-(-14))/(-10-(-8)) = -3/-2 = 3/2

FOR THE NEXT PART I'LL DO 7,8 AND 10 FOR YOU, TRY DOING 9 ON YOUR OWN FOR PRACTICE.

I WILL ALSO ATTACH FILES FOR THE NEXT PARTS IN ORDER OF QUESTIONS SO SEE THEM.

7. y = x + 3 this means y = 1x +3 which means:

1 is the gradient

3 is the y-intercept

so 1 as a fraction is 1/1 which means rise is one upwards and run is 1 to the right.

Now go to the graph on the y-axis and plot the point 3, (0,3) is your y-intercept. From their rise by one and run by one this will lead u to point (1,4)

Mark both these points and make a line through them.

8. x = -5

now look at this equation in the form of y = mx + c

0 = 1x + 5 the means y is 0 and it is already told in the question that x = -5

if u rearrange 0 = 1x + 5 it will give you x = -5

now when y is  0 x = -5 put a point on the coordinate (-5,0) and draw a vertical straight line.

10. y = (1/4)x - 1

slope is 1/4 which means rise is 1 and run is 4

y-intercept is -1

now go to y=-1 which is the coordinate (0,-1) and rise by one and run by 4, this will take u to the coordinate (4,0) now put a dot on both coordinates, connect them and put a line through them.