Question

1) Graph the following lines and using the graph determine several values of x for which the graph is positive (negative):

y=−0.5x−2

2) Find the coordinates of the points of intersection of the graphs with coordinate axes:
y=−1.5x+3

3) Find the coordinates of the points of intersection of the graph of y=13−x with the axes and compute the area of the right triangle formed by this line and coordinate axes.

4) Find the coordinates of the point of intersection of the graphs of lines:
y=−2x+7 and y=0.5x−5.5

5) Construct the triangle ABC using as coordinates of its vertices points A(−3, 0), B(4, 5),
C(0, −4). Find the coordinates of intersection of side AB with the y-axis.

If you don't get some of them, it's fine, can you just help me with the ones that you get???
Show work for the ones you answer please!!!!

Answer 1

Answer: (0, 2 1/7) or (0, 15/7)

Explanation:

For number 5

Answer 2

1)
`y=-0.5x-2`

The graph of the above equation is attached in the attachment below.

For all the values from negative infinity to -4, the function is positive.

X ∈ (-∞,-4]

2)
`y=-1.5x+3`

To find the x- intercept, plug y =0

`0=-1.5x+3`

`1.5x=3`

`x=2`

x intercept = (2,0)

To find the y- intercept, plug x=0

`y=-1.5(0)+3`

`y=3`

Y- intercept = ( 0,3)

3)
`y=13-x`

Y- intercept = (0,13)

x- intercept = (13,0)

Area of triangle =
`(bh)/(2)`

Area of triangle =
`(13*13)/(2)`

Area =
`(169)/(2)` sq unit.

4) The graphs of
`y=-2x+7` and
`y=0.5x-5.5` is attached in the attachment below.

The intersection point is ( 5,-3)

5) A = (-3,0)

B = (4,5)

C = (0,-4)

Slope of AB =
`(5-0))/(4-(-3)) =(5)/(7)`

Slope intercept of line
`y=mx+b`

Where, m is the slope and b is the y- intercept.

Plugging point A and the slope in the y- intercept to find the value of b.

`0=(5(-3))/(7) +b`

`b=(15)/(7)`

Equation of line AB:
`y=(5x)/(7) +(15)/(7)`

Slope of BC =
`(-4-5)/(0-4) =(9)/(4)`

Plug C = (0,-4)

`-4=0+b`

b=-4

equation of line BC=
`y=(9x)/(4) -4`

Slope of line AC =
`(-4-0)/(0--3) =(-4)/(3)`

Equation of line AC =
`y=(-4x)/(3) -4`

Y intercept of AB =
`(0,(15)/(7) )`