Question

8. The table below contains points that lie on a line a) Fill in the missing table values. Х 5 2 -1 -10 -19 다. 4 8 20 | 24 32 b) Find the slope of the line that passes through the ports

Answer 1

The missing table values include the following;

x 5 -7 -13

y 0 8/3 24

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

`y - y_1 = m(x - x_1)`

Where:

x and y represent the data points.

m represent the slope.

First of all, we would determine the slope for the line;

`Slope(m)=(y_2-y_1)/(x_2-x_1)`

Slope (m) = (8 - 4)/(-1 - 2)

Slope (m) = -4/3

At data point (-1, 8) and a slope of -4/3, a function for this line can be calculated by using the point-slope form as follows:

y - 8 = -4/3(x + 1)

y = -4/3(x) + 20/3

When x is 5, the value of y is given by;

y = -4/3(5) + 20/3

y = -20/3 + 20/3

y = 0

When x is -7, the value of y is given by;

y = -4/3(-7) + 20/3

y = 28/3 + 20/3

y = 8/3

When y is 24, the value of y is given by;

24 = -4/3(x) + 20/3

24 -20/3 = -4/3(x)

52/3 = -4x/3

x = -13

Answer 2

step 1

Find the slope of the line

we need two points

take the points (2,4) and (-1,8)

m=(8-4)/(-1-2)

m=4/-3

m=-4/3

step 2

Find the equation of the line in point slope form

y-y1=m(x-x1)

we have

m=-4/3

(x1,y1)=(2,4)

substitute

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

step 3

Convert to slope intercept form

y=mx+b

isolate the variable y

y-4=(-4/3)x+8/3

y=(-4/3)x+(8/3)+4

y=(-4/3)x+20/3

step 4

Fill the table

For x=5

substitute in the linear equation

y=(-4/3)(5)+20/3

y=0

For x=-7

substitute

y=(-4/3)(-7)+20/3

y=28/3+20/3

y=48/3

y=16

For y=24

substitute

24=(-4/3)x+20/3

solve for x

(4/3)x=20/3-24

(4/3)x=-52/3

4x=-52

x=-13