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

1 answer:

8 0

<h3>Explanation</h3>

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

Note: Origin point = (0,0).

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

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

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

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

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

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

Therefore we rewrite the equation again to

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

<h3>Answer</h3>

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

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worty [1.4K]

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3 years ago

timurjin [86]

If the unknown value is x, then x = $\frac{14}{4}$ × 6 = 21.

Explanation:

Since it is a double number line with a ratio, all the ratios of one number line to the other will remain equal for all the values along both the number lines. Assume the unknown value to be x.
The ratio of the number on the first number line to the corresponding number on the second number line is calculated to be; $\frac{7}{2}$ = $\frac{14}{4}$ = $\frac{x}{6}$ = $\frac{28}{8}$ = $\frac{35}{10}$ = 3.5. So $\frac{x}{6}$ = 3.5, x = 3.5 × 6 = 21.
We can also calculate x by the following method. As ratios are equal we can directly substitute the value to another ration. So $\frac{14}{4}$ = $\frac{x}{6}$ , x = $\frac{14}{4}$ × 6 = $\frac{84}{4}$ = 21.