Question

Graph the line using a point and a slope. Write the equation of each line.

Answer 1

Answer:

  y = -1/2x -3

Step-by-step explanation:

The line perpendicular to one with a slope of 2 will have a slope that is the negative reciprocal of 2, that is, -1/2. The given point is the y-intercept of the required line, so we can write its equation directly in slope-intercept form:

  y = mx + b

where m is the slope (-1/2), and b is the y-intercept (-3). Your line is ...

  y = -1/2x -3

Answer 2

Answer:

$y=-\frac{x}{2}-3$

Step-by-step explanation:

If two lines having slopes $m_1$ and $m_2$ are perpendicular,

$m_1\times m_2=-1$

Thus, if the slope of the line perpendicular line with slope 2 is m,

Then,

$m\times 2=-1\implies m = -\frac{1}{2}$

Now, the equation of the line passes through $(x_1, y_1)$ with slope m is,

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

Hence, the equation of the line contain (0, -3) with slope $-\frac{1}{2}$ is,

$y+3=-\frac{1}{2}(x-0)$

$y=-\frac{1}{2}x-3$

Graphing :

if x = 0, y = -3,

if y = 0, $-\frac{x}{2}=3$ ⇒ x = -6

Thus, by joining the points (0, -3) and (-6, 0) we will get the graph of the given line.