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3 years ago

Which equation represents the line that passes through points (1, –5) and (3, –17)?

Mathematics

1 answer:

Serjik [45]3 years ago

3 0

Answer:

Step-by-step explanation:

I’m rusty with my math, so I’m not 100% sure this is correct. My best attempt.

(1,-5) & (3,-17)

1=1x, -5=1y, 3=2x, -17=2y

Formula is y2-y1/x2-x1

-17 - -5 = -12

3 - 1 =2

So -12/2 = -6

Formula for the line is

y-y1 = m (x-x1)

In this equation m=-6

Y - -5 = -6 ( x - 1 )

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Write a system of linear inequalities so the points (1, 2) and (4, -3) are solutions of the system, but the point (-2, 8) is not

Verizon [17]

Answer: $\left \{ {{y\leq -\frac{5}{3}x + \frac{11}{3}} \atop {y < 8}} \right$

<u>Step-by-step explanation:</u>

(1, 2) and (4, -3)

First, find the slope (m): $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

m = $\frac{-3-2}{4-1}$

= $-\frac{5}{3}$

Next, choose ONE of the points and input the point and slope into the Point-Slope formula: y - y₁ = m(x - x₁)

y - 2 = $-\frac{5}{3}$ (x - 1)

y - 2 = $-\frac{5}{3}x$ + $\frac{5}{3}$

y = $-\frac{5}{3}x$ + $\frac{11}{3}$

Then, determine which inequality symbol will result in (-2, 8) being False (since it is not a solution):

y ___ $-\frac{5}{3}x$ + $\frac{11}{3}$

8 ___ $-\frac{5}{3}(-2)$ + $\frac{11}{3}$

8 ___ $\frac{1}{3}$

8 > $\frac{1}{3}$

so ≤ makes the statement False

⇒ y ≤ $-\frac{5}{3}x$ + $\frac{11}{3}$

****************************************************************

If you need a "system" of inequalities, then you need another equation.

There are infinite possibilities. Graph the points to see what works.

y < 8 or x > -2 are two examples.

---> I just realized that the system can be simpler than what I did above:

$\left \{ {{x>-2} \atop {y < 8}} \right$

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