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4 years ago

What is the y-intercept? Give explanation, please.

Mathematics

1 answer:

vlada-n [284]4 years ago

4 0

Answer:

$y = \frac{4}{5}x - 2 → y = \frac{4}{5}x + -2 \\ \\ -2 = b$

Step-by-step explanation:

First, check the rate of change [slope]:

$\frac{-y_1 + y_2}{-x_1 + x_2} = m$

$\frac{-2 + 6}{-5 + 10} = \frac{4}{5}$ ☑

Then plug these coordinates into the Slope-Intercept Formula instead of the Point-Slope Formula, to get it done much swiftly. It does not matter which ordered pair you choose:

6 = ⅘[10] + b

$−2 = b$

$y = \frac{4}{5}x - 2$

_______________________________________________

2 = ⅘[5] + b

−2 = b

$y = \frac{4}{5}x - 2$

** You see? I told you it did not matter which ordered pair you choose because you will ALWAYS get the exact same result.

I am joyous to assist you anytime.

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What is the sum of the first five terms of a geometric series with a1 = 6 and r = 1/3?

tresset_1 [31]

The sum of the terms of a geometric sequence with common ratio lesser than 1 is calculated through the equation,

Sn = (a1) x (1 - r^n) / (1 - r)
Substituting the known values,
S5 = (6) x (1 - (1/3)^5) / (1 - 1/3) = 242/27
Thus, the sum of the first five terms is approximately equal to 8.96.

6 0

3 years ago

Read 2 more answers

Write an equation of a parabola that passes through (3,-30) and has x-intercepts of -2 and 18. Then find the average rate of cha

Nookie1986 [14]

Answer:

The equation of the parabola is $y = \frac{2}{5}\cdot x^{2}-\frac{32}{5}\cdot x -\frac{72}{5}$ . The average rate of change of the parabola is -4.

Step-by-step explanation:

We must remember that a parabola is represented by a quadratic function, which can be formed by knowing three different points. A quadratic function is standard form is represented by:

$y = a\cdot x^{2}+b\cdot x + c$

Where:

$x$ - Independent variable, dimensionless.

$y$ - Dependent variable, dimensionless.

$a$ , $b$ , $c$ - Coefficients, dimensionless.

If we know that $(3, -30)$ , $(-2, 0)$ and $(18, 0)$ are part of the parabola, the following linear system of equations is formed:

$9\cdot a +3\cdot b + c = -30$

$4\cdot a -2\cdot b +c = 0$

$324\cdot a +18\cdot b + c = 0$

This system can be solved both by algebraic means (substitution, elimination, equalization, determinant) and by numerical methods. The solution of the linear system is:

$a = \frac{2}{5}$ , $b = -\frac{32}{5}$ , $c = -\frac{72}{5}$ .