Question

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

Answer 1

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

Step-by-step 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 = $\frac{bh}{2}$

Area of triangle = $\frac{13\times13}{2}$

Area = $\frac{169}{2}$ 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 = $\frac{5-0)}{4-(-3)} =\frac{5}{7}$

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.  

$0=\frac{5(-3)}{7} +b$

$b=\frac{15}{7}$

Equation of line AB: $y=\frac{5x}{7} +\frac{15}{7}$

Slope of BC = $\frac{-4-5}{0-4} =\frac{9}{4}$

Plug C = (0,-4)  

$-4=0+b$

b=-4

equation of line BC= $y=\frac{9x}{4} -4$

Slope of line AC = $\frac{-4-0}{0--3} =\frac{-4}{3}$

Equation of line AC = $y=\frac{-4x}{3} -4$

Y intercept of AB = $(0,\frac{15}{7} )$