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3 years ago

Choose the equation below that represent the line passing through the point (-2,-3) With a slope of -6

Mathematics

2 answers:

Gnom [1K]3 years ago

5 0

Y+3= -6 (x+2) is the correct equation

Len [333]3 years ago

4 0

Answer:

The equation of line is (y+3)=-6(x+2).

Step-by-step explanation:

It is given that the line passing through the point (-2,-3) with a slope of -6.

If a line passes through a point $(x_1,y_1)$ , then point slope form of the line is

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

where, m is slope of the line.

Substitute $x_1=-2,y_1=-3$ and m=-6 in the above equation.

$(y-(-3))=-6(x-(-2))$

On simplification we get

$(y+3)=-6(x+2)$

Therefore the equation of line is (y+3)=-6(x+2).

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Find the equation of a line that passes through (0,0) that is perpendicular to 2x+3y=-6

Dovator [93]

The slope-intercept form of a line:

$y=mx+b$

m - slope

b - y-intercept

Convert 2x + 3y = -6 to the slope-intercet form:

$2x+3y=-6$ <em>subtract 2x from both sides</em>

$3y=-2x-6$ <em>divide both sides by 3</em>

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

Let $k:y=m_1x+b_1$ and $l:y=m_2x+b_2$

$l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}$

We have $m_1=-\dfrac{2}{3}$

Therefore

$m_2=-\dfrac{1}{-\frac{2}{3}}=\dfrac{3}{2}$

We have the equation of a line:

$y=\dfrac{3}{2}x+b$

Put the coordinates of the point (0, 0) to the equation:

$0=\dfrac{3}{2}(0)+b$

$0=b\to b=0$

Answer: $\boxed{y=\dfrac{3}{2}x}$

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