Mathematics: Which is an equation of the line through the origin and (-4,-9)?

Which is an equation of the line through the origin

nikitakhrabkov123

18.03.2022

ExplanationCalculate the slope by using the rise over run with two given coordinate points.

Note: Origin point = (0,0).

$\begin{cases}(x_1, y_1) = ( - 4, - 9) \\ (x_2, y_2) = ( 0, 0) \end{cases}$

$m = \frac{y_2 - y_1}{x_2 - x_1} \\ m = \frac{0 - ( - 9)}{0 - ( - 4)} \\ m = \frac{0 + 9}{0 + 4} \Longrightarrow \frac{9}{4}$

Slope-Intercept

$y = mx + b \\ \begin{cases} \sf{m = slope} \\ \sf{b = y - intercept} \end{cases}$

Rewrite the equation by substituting m = 9/4 in the equation.

$y = \frac{9}{4} x + b$

Find the value of b.

Because the graph passes through the origin point. That means the y-intercept is (0,0).

Therefore we rewrite the equation again to

$y = \frac{9}{4} x + 0 \\ y = \frac{9}{4} x$

Answer

$\large \boxed{y = \frac{9}{4} x}$

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Fredo10

04.11.2021

a. ∫ xSinx dx

iii. integration by parts

u =x and dv= sinx

b. ∫ x⁴/(1+x³). dx

ii. neither

Long division is an option here before integration is done

c. ∫ x⁴. e^x³. dx

i. substitution

where u = x⁵

d. ∫x⁴ cos(x⁵). dx

i. substitution

where u = x⁵

e. ∫1/√9x+1 .dx

i. substitution

where u = 9x+1

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