Question

equations - draw right triangles to calculate the slope and write a proportional equation
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solve problems
1 use the points on the line to draw a right triangle and calculate the slope. then, write an equation for this proportional relationship.
slope = \frac{\square - \square}{\square - 0}=\frac{\square}{\square}=\square
y = \square x
2 use the points on the line to draw a right triangle and calculate the slope. then, write an equation for this proportional relationship.
slope = \frac{2 - \square}{\square - \square}=\frac{\square}{\square}=\square
y = \square x
3 use the points on the line to draw a right triangle and calculate the slope. then, write an equation for this proportional relationship.
slope = \frac{\square - \square}{\square - 0}=\frac{\square}{\square}=\square
y = \square x
4 use the points on the line to draw a right triangle and calculate the slope. then, write an equation for this proportional relationship.
slope = \frac{\square - \square}{8 - \square}=\frac{\square}{\square}=\square
y = \square x

Explanation:

Step1: Identify two points for problem 1

Let the two - points be $(0,0)$ and $(2,5)$.

Step2: Calculate the slope for problem 1

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. So, $m=\frac{5 - 0}{2 - 0}=\frac{5}{2}$.

Step3: Write the proportional equation for problem 1

For a proportional relationship $y = mx$, so $y=\frac{5}{2}x$.

Step4: Identify two points for problem 2

Let the two - points be $(0,0)$ and $(4,2)$.

Step5: Calculate the slope for problem 2

Using the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, we have $m=\frac{2 - 0}{4 - 0}=\frac{2}{4}=\frac{1}{2}$.

Step6: Write the proportional equation for problem 2

For a proportional relationship $y = mx$, so $y=\frac{1}{2}x$.

Step7: Identify two points for problem 3

Let the two - points be $(0,0)$ and $(3,9)$.

Step8: Calculate the slope for problem 3

Using the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, we get $m=\frac{9 - 0}{3 - 0}=3$.

Step9: Write the proportional equation for problem 3

For a proportional relationship $y = mx$, so $y = 3x$.

Step10: Identify two points for problem 4

Let the two - points be $(0,0)$ and $(8,4)$.

Step11: Calculate the slope for problem 4

Using the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, we have $m=\frac{4 - 0}{8 - 0}=\frac{4}{8}=\frac{1}{2}$.

Step12: Write the proportional equation for problem 4

For a proportional relationship $y = mx$, so $y=\frac{1}{2}x$.

Answer:

Problem 1:
slope = $\frac{5 - 0}{2 - 0}=\frac{5}{2}$; $y=\frac{5}{2}x$
Problem 2:
slope = $\frac{2 - 0}{4 - 0}=\frac{1}{2}$; $y=\frac{1}{2}x$
Problem 3:
slope = $\frac{9 - 0}{3 - 0}=3$; $y = 3x$
Problem 4:
slope = $\frac{4 - 0}{8 - 0}=\frac{1}{2}$; $y=\frac{1}{2}x$