Question

Please Help me plz! Thanks

Answer 1

Option D:

The equation of a line in point-slope form is y = 3x – 7.

Solution:

Take any two points on the line given in the graph.

Let the points be (–4, 4) and (2, 2).

$x_1=-4, y_1=4, x_2=2, y_2=2$

Slope of the given line:

$m_1=\frac{y_2-y_1}{x_2-x_1}$

$m_1=\frac{2-4}{2-(-4)}$

$m_1=\frac{-2}{6}$

$m_1=\frac{-1}{3}$

If two lines are perpendicular, then the product of their slopes are –1.

$\Rightarrow m_1\times m_2=-1$

$\Rightarrow \frac{-1}{3} \times m_2=-1$

Multiply by 3 on both sides of the equation.

$\Rightarrow- m_2=-3$

Multiply by –1 on both sides of the equation.

⇒ $m_2=3$

Perpendicular line passes through the point (2, –1).

Here, $x_1=2, y_1=-1$.

Using point-slope form:

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

$y-(-1)=3(x-2)$

$y+1=3x-6$

Subtract 1 on both sides of the equation.

$y=3x-7$

The equation of a line in point-slope form is y = 3x – 7.

Therefore option D is the correct answer.