Question

Write the equation of the line that is parallel to the given segment and that passes through the point (-3,0).

Answer 1

Answer:

Option (B)

Step-by-step explanation:

In the figure attached,

A straight line is passing through two points (0, 2) and (3, 1).

Slope of this line ($m_1$) = $\frac{y_2-y_1}{x_2-x_1}$

                                   = $\frac{2-1}{0-3}$

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

Let the slope of a parallel to the line given in the graph = $m_2$

By the property of parallel lines,

$m_1=m_2$

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

Equation of a line passing through a point (x', y') and slope 'm' is,

y - y' = m(x - x')

Therefore, equation of the parallel line which passes through (-3, 0) and having slope = $-\frac{1}{3}$ will be,

$y-0=-\frac{1}{3}(x+3)$

$y=-\frac{1}{3}x-1$

Option (B). will be the answer.