Question

the relationship between money earned and hours worked is linear. joe computes the slope between (4, 30) and (12, 90), then computes the slope between (4, 30) and (10, 75). how do the two slopes compare?

Answer 1

Slope = rise/run =[y2-y1]/[x2-x1]

1) slope = [90 - 30] / [12 - 4] = 60 / 8 = 15/2

2) slope = [75 - 30] / [10 - 4] = 45 / 6 = 15 / 2

The slopps are equal.

Answer 2

Answer: The slopes are equal.

The points are representing the same line.

Step-by-step explanation:

We know that the slope between points (a,b) and (c,d) is given by :-

$m=\dfrac{d-b}{c-a}$

The slope between the points (4,30)  and (12,90) will be

$m_1=\dfrac{90-30}{12-4}=\dfrac{60}{8}=\dfrac{15}{2}$

The slope between the points (4,30) and (10,75) will be

$m_2=\dfrac{75-30}{10-4}=\dfrac{45}{6}=\dfrac{15}{2}$

$\Rightarrow\ m_1=m_2$

We know that if the slopes are equal then the lines are parallel.

But they have one point common (4,30) so it cannot be parallel, they ust be same line .