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3 years ago

Write an equation in point-slope form for the line through the given point with the given slope. (–3, –7); m = -6/5x

Mathematics

1 answer:

PSYCHO15rus [73]3 years ago

8 0

Answer: y= -6/5x - 53/5

Step-by-step explanation:

y - y₁ = m(x - x₁)

y - (-7) = -6/5(x- (-3))

y + 7 = -6/5(x + 3)

y+ 7= -6/5x - 18/5

y = -6/5x - 18/5 - 7

y = - 6/5x - 53/5

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Find the equation of the line that contains the given point and the given slope. Write the equation in slope-intercept form.

stealth61 [152]

The slope-point form of a line:

$y-y_0=m(x-x_0)$

The slope-intercept form of a line:

$y=mx+b$

$m=6,\ (4,\ 1)\to x_0=4,\ y_0=1$

Substitute

$y-1=6(x-4)\qquad|\text{use distributive property}\\\\y-1=6x-24\qquad|\text{add 1 to both sides}\\\\\boxed{y=6x-23}$

$m=-5,\ (6,\ -3)$

Substitute

$y-(-3)=-5(x-6)\qquad|\text{use distributive property}\\\\y+3=-5x+30\qquad|\text{subtract 5 from both sides}\\\\\boxed{y=-5x+24}$

$m=-\dfrac{1}{2},\ (-8,\ 2)\\\\y-2=-\dfrac{1}{2}(x-(-8))\\\\y-2=-\dfrac{1}{2}(x+8)\\\\y-2=-\dfrac{1}{2}x-4\qquad|\text{add 2 to both sides}\\\\\boxed{y=-\dfrac{1}{2}x-2}$

$m=0,\ (-7,\ -1)\\\\y-(-1)=0(x-(-7))\\\\y+1=0\qquad|\text{subtract 1 from both sides}\\\\\boxed{y=-1}$

3 0

3 years ago

Given cosθ=√3/3 and sinθ<0. What is the value of sinθ?

KATRIN_1 [288]

$\sin^{2} \theta+\cos^{2} \theta=1 \\ \\ \sin^{2} \theta+\left(\frac{\sqrt{3}}{3} \right)^{2}=1 \\ \\ \sin^{2} \theta+\frac{1}{3}=1 \\ \\ \sin^{2} \theta=\frac{2}{3} \\ \\ \theta=-\frac{\sqrt{2}}{\sqrt{3}}=\boxed{-\frac{\sqrt{6}}{3}}$

5 0

2 years ago

Jack's brother is 14 years older than him. In six years time, Jack's brother will be twice as old as him. How old is Jack now?

mr Goodwill [35]

14+14 is 28 28-6 is 22 so Jack is 22

3 0

3 years ago

A shipping container will be used to transport several 120-kilogram crates across the country by rail. The greatest weight that

Kitty [74]

Answer:

101

Step-by-step explanation:

The leftover weight that can be put onto the container (x)

x = 24500 - 12300

x = 12200

The amount of crates that can be hauled into the container

x = 12200 / 120

= 101.6667

We need a whole number so we round down.

= 101

5 0

3 years ago

How do I solve this?

Anit [1.1K]

not a clue luv sorry xxxx

4 0

4 years ago