choose two points for a straight line so that the slope becomes -0.25.
this is all i'm given but i don't understand what it means. Do I pick two points and make a formula? wouldnt the slope be 0.25x + 1 lets say and you can get points by plugging in x?
Yes : )
You know that -0.25 means your line is slanting downwards when looked at from the left most point to the right most point.
And you also know that 0.25 as a fraction is 1/4
so your slope from the first point to the next point is ... down one unit, and move to the right 4 units... and plot a second point : )
just work backwards
slope = -.25 = -1/4
slope = change in y/change in x
so all you need is a pair of numbers with a difference of -1
and another pair with a difference of 4
for the first one, how about 5 - 6 <----- those are y's
for the 2nd , how about 7-3 <---- those are x's
so (3,6) and (7,5) would do.
Of course there would be an infinite number of such combinations
OR
you could just take any equation of the form y = (-1/4)x + b
put in anything you want for b, how about
y = (-1/4)x + 5
now pick any x, preferably a multiple of 4 to avoid fraction, and get the y
e.g. let x = 8, then y = (-1/4)(8) + 5 = 3 ----> point (8,3)
let x = -4, then y = (-1/4)(-4) + 5 = 6 ----> point (-4,6)
check: slope = (3-6)/(8+4) = -3/12 = -1/4
To choose two points for a straight line with a specific slope, you need to understand the slope-intercept form of a linear equation, which is commonly represented as y = mx + b. In this equation, "m" represents the slope of the line.
To find two points for a line with a slope of -0.25, you can follow these steps:
1. Choose an arbitrary value for x. Let's say you pick x = 0.
2. Plug the value of x into the equation y = -0.25x + b.
Thus, it becomes y = -0.25(0) + b, which simplifies to y = b.
3. The value of y when x = 0 is equal to the y-intercept, denoted as b. Therefore, one point on the line is (0, b).
Now, let's find another point to determine the line completely:
4. Choose another value for x. For simplicity, let's select x = 1.
5. Plug the value of x into the equation y = -0.25x + b.
It becomes y = -0.25(1) + b = -0.25 + b.
6. Since we need the slope to be -0.25, we can equate this to the previous value of y.
-0.25 + b = b.
7. Solve for b by subtracting b from both sides of the equation:
-0.25 = 0b.
8. We find that b = -0.25.
Therefore, the second point on the line is (1, -0.25).
In conclusion, the two points for a straight line with a slope of -0.25 are (0, b) and (1, -0.25), where b is the y-intercept.