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Graph the line using a point and a slope. Write the equation of each line.
C) a line that contains point (0, −3) and perpendicular to another line whose slope is 2.

Respuesta :

sqdancefan

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

Ver imagen sqdancefan

Answer:

[tex]y=-\frac{x}{2}-3[/tex]

Step-by-step explanation:

If two lines having slopes [tex]m_1[/tex] and [tex]m_2[/tex] are perpendicular,

[tex]m_1\times m_2=-1[/tex]

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

Then,

[tex]m\times 2=-1\implies m = -\frac{1}{2}[/tex]

Now, the equation of the line passes through [tex](x_1, y_1)[/tex] with slope m is,

[tex]y-y_1=m(x-x_1)[/tex]

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

[tex]y+3=-\frac{1}{2}(x-0)[/tex]

[tex]y=-\frac{1}{2}x-3[/tex]

Graphing :

if x = 0, y = -3,

if y = 0, [tex]-\frac{x}{2}=3[/tex] ⇒ x = -6

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

Ver imagen slicergiza

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