1. m = 4 (1,2)
m = slope
f'(x) = slope
In order to acquire back the original function, we need to integrate the slope.
∫4 dx = 4x + c
Since we do not know the value of our constant of integration, we can simply assume that our equation would be y = 4x.
[tex]Answer: y = 4x[/tex]
2. (5,-3) and (3,5)
The interval of our x values from the left side of our number line to the right side would be 2. Therefore, 2 is our run and for our rise is -8. In this case our slope would be the ratio of our rise run. Slope = -8/2 = -4. Since our equation is a linear, we can simply assume that our equation would be y = -4x.
[tex]Answer: y = - 4x[/tex]
3. (5,0) and (0,7)
The interval of our x values from the left side of our number line to the right side would be 5. Therefore, 5 is our run and for our rise is -7. In this case our slope would be the ratio of our rise run. Slope = -7/5. Since our equation is a linear, we can simply assume that our equation would be y = -(7/5)x.
[tex]Answer: y = - \frac{7}{5} x[/tex]
4. m = -1/4, (7,0)
m = slope
f'(x) = slope
In order to acquire back the original function, we need to integrate the slope.
∫-1/4 dx = -1/4x + c
Since we do not know the value of our constant of integration, we can simply assume that our equation would be y = -1/4x.
[tex]Answer: y = - \frac{1}{4} x[/tex]
5. (-9,-1) and (-9,0)
The value of our x in these two ordered pairs are both the same but their y values are not the same. In this case I can conclude that the graph is a line in vertical orientation.
[tex]Answer: x = - 9[/tex]
6. x-intercept of 4 and y-intercept of -1
y = mx + b
let X = 0, y intercept = -1
let Y = 0, x intercept = 4
y = mx + b
(+1) 0 = mx - 1 (+1)
1 = mx
1/x = m
(y=0, x= 4) substitute;
1/4 = slope.
Therefore, the equation would be y = 1/4x
[tex]Answer: y = \frac{1}{4} x[/tex]
