The following graph shows a proportional relationship.

Mathematics

1 answer:

elena-s [515]2 years ago

8 0

Answer:

The constant of proportionality is thus 1

Step-by-step explanation:

Note that the green line passes through (6, 6) and has a y-intercept of 0. Thus, the equation of the line is y = (6/6)x + 0, or y = x, or y = 1x.

The constant of proportionality is thus 1, which is also the slope of this line.

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Find the slope between these two points: (3, -10) and (-2, -30). Show all of your work. what the answer

Harlamova29_29 [7]

$\huge\text{$m=\boxed{4}$}$

Hey there! Start with the slope formula, where $(x_1,y_1)$ and $(x_2,y_2)$ are the two known points.

$\begin{aligned}m&=\dfrac{y_2-y_1}{x_2-x_1}\\&=\frac{-30-(-10)}{-2-3}\end{aligned}$

Simplify.

$\begin{array}{c|l}\textbf{Solving}&\textbf{Reason}\\\cline{1-2}\\m=\dfrac{-30+10}{-2-3}&x-(-y)=x+y\\\\m=\dfrac{-20}{-5}&\text{Addition and subtraction}\\\\m=\dfrac{20}{5}&\text{The negatives cancel out}\\\\m=\dfrac{4}{1}&\text{Divide the numerator and denominator by $5$}\\\\m=\boxed{4}&\dfrac{x}{1}=x\end{aligned}$