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:
[tex]\begin{gathered} (2,-3) \\ (2+1,-3-5)=(3,-8) \\ (2-1,-3+5)=(1,2) \end{gathered}[/tex]
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:
[tex]\begin{gathered} (1,2) \\ (1-1,2+5)=(0,7) \end{gathered}[/tex]
So the y-intercept is (0, 7)
c) Using the slope m = -5 and the y-intercept b = 7, the equation is:
[tex]y=-5x+7[/tex]
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.
