Question

Plot the point the. Make a staircase using the given slope connect the points to form a line. Answer the questions below

Answer 1

In order to create a staircase with the points, let's find 2 more points of the line.

The slope of -5 indicates that each unitary increase in x causes a decrease of 5 units in y.

So starting from (2, -3), we can add one unit to x and subtract one unit from x:

`\begin{gathered} (2,-3) \\ (2+1,-3-5)=(3,-8) \\ (2-1,-3+5)=(1,2) \end{gathered}`

Graphing these points and the corresponding line, we have:

a)

The line is decreasing (because of the negative slope)

b)

The y-intercept is the point where x = 0. Using the point (1,2) and subtracting one unit to x (therefore adding 5 units to y), we have:

`\begin{gathered} (1,2) \\ (1-1,2+5)=(0,7) \end{gathered}`

So the y-intercept is (0, 7)

c) Using the slope m = -5 and the y-intercept b = 7, the equation is:

`y=-5x+7`

d)

y2 = -5x + 7

e)

Our line is steeper than y = x, since the absolute value of the slope is greater than the slope of y = x (which is 1)

f)

Our line is higher than y = x in the y-axis, because the y-intercept is 7, and the y-intercept of y = x is 0.

g)

We can see the negative value of the slope (-5), indicating that if we increase the value of x, the value of y decreases.