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3 years ago

How many solutions does the equation have 3 + 5n = 5(n + 2) - 7

Mathematics

1 answer:

krok68 [10]3 years ago

3 0

Answer: an infinite amount of answers

Step-by-step explanation:

It’s all real numbers from negative infinity to positive infinity

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A line is graphed below. Write an equation in the form y = mx + b that represents this line

galben [10]

<h3>Explanation</h3>

Slope-Intercept form

$y = mx + b \\ m = slope \\ b = y - intercept$

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

$\begin{cases}(x_1,y_1) = ( - 4,0) \\ (x_2,y_2) = ( 0,2) \end{cases}$

These two coordinate points are part of the graph and can be used to find the slope.

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

Substitute the coordinate points in the formula.

$m = \frac{2 - 0}{0 - ( - 4)} \\ m = \frac{2}{ 4} \\ m = \frac{1}{2}$

Therefore, the slope is 2.

Rewrite the equation in slope-intercept.

$y = \frac{1}{2} x + b$

Calculate the y-intercept by substituting any given points in new rewritten equation.

$(x,y) = ( 0,2)$

I will be substituting these coordinate points in the equation.

$y = \frac{1}{2} x + b$

Substitute x = 0 and y = 5 in the equation.

$2 = \frac{1}{2} (0) + b \\ 2 = 0 + b \\ 2 = b$

Therefore the y-intercept is (0,2).

Rewrite the equation.

$y = \frac{1}{2} x + 2$

<h3>Answer</h3>

 $\large \boxed{y = \frac{1}{2} x + 2}$ 

If you have any questions related to the answer, feel free to ask me via comment.

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3 years ago