Question

Need help to solve this problem. It is very hard. Can u figure it out. I have no idea

Answer 1

a) Given the equation of line m below

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

Using a graphing tool, the graph of line m is shown below

The line is labeled m

b) A line, p, is parallel to line m and passes through point (3, 4)

The slope of parallel lines is equal.

Thus, the slope of line p is 2/3

To find the equation of line p, the formula is

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

Substitute the coordinates and the slope into the formula above

`\begin{gathered} (y-4)=(2)/(3)(x-3) \\ y-4=(2)/(3)x-2 \\ Collect\text{ like terms} \\ y=(2)/(3)x-2+4 \\ y=(2)/(3)x+2 \end{gathered}`

The graph of line p, is shown below

c) The equation of line p in slope-intercept form is

`y=(2)/(3)+2`

d) Line s is perpendicular to line m,

To find the slope of a perpendicular line, the formula is

`\begin{gathered} m_1\cdot m_2=-1 \\ Where \\ The\text{ slope of line }m,\text{ }m_1=(2)/(3) \\ The\text{ slope of line s is }m_2 \\ (2)/(3)\cdot m_2=-1 \\ m_2=-(3)/(2) \end{gathered}`

And line s passes through the point (0, -4),

The equation of line will be

`\begin{gathered} (y-y_1)=m_2(x-x_1) \\ y-(-4)=-(3)/(2)(x-0) \\ y+4=-(3)/(2)x \\ Collect\text{ like terms} \\ y=-(3)/(2)x-4 \end{gathered}`

The graph of line s is shown below

e) The equation of line s in slope intercept form is

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

f) To justify if line s is perpendicular to line p,

Using their slopes

`\begin{gathered} Slope\text{ of line }s,\text{ }m_1=-(3)/(2) \\ Let\text{ }m_2\text{ be the slope of line p} \\ For\text{ perpendicular lines} \\ m_1\cdot m_2=-1 \\ -(3)/(2)\cdot m_2=-1 \\ (-3m_2)/(2)=-1 \\ -3m_2=-2 \\ m_2=(-2)/(-3)=(2)/(3) \\ The\text{ slope of }m_2=(2)/(3) \end{gathered}`

Hence, line s is perpendicular to line p