QUESTION 1
We want to find the slope through the points (12,-18), (11,12).
We use the slope formula,
![m = \frac{y_2-y_1} {x _2-x_1}](https://tex.z-dn.net/?f=m%20%3D%20%20%5Cfrac%7By_2-y_1%7D%20%7Bx%20_2-x_1%7D%20)
We substitute the points to get,
![m = \frac{12 - - 18}{11 - 12}](https://tex.z-dn.net/?f=m%20%3D%20%20%5Cfrac%7B12%20-%20%20-%2018%7D%7B11%20-%2012%7D%20)
![m = \frac{30}{ - 1} = - 30](https://tex.z-dn.net/?f=m%20%3D%20%20%5Cfrac%7B30%7D%7B%20-%201%7D%20%20%3D%20%20-%2030)
The slope is -30.
QUESTION 2.
We want to find the slope through the points (-18, -20), (-18, -15).
We use the slope formula again to obtain,
![m = \frac{ - 15 - - 20}{ - 18 - - 18}](https://tex.z-dn.net/?f=m%20%3D%20%20%5Cfrac%7B%20-%2015%20-%20%20-%2020%7D%7B%20-%2018%20-%20%20-%2018%7D%20)
We simplify to get;
![m = \frac{5}{0}](https://tex.z-dn.net/?f=m%20%3D%20%20%5Cfrac%7B5%7D%7B0%7D%20)
Division by zero means the slope is not defined.
QUESTION 3
The given equation is 4x + y = 5.
At x-intercept, y=0.
We put y=0 into the equation to get,
![4x + 0 = 5](https://tex.z-dn.net/?f=4x%20%2B%200%20%3D%205)
![4x = 5](https://tex.z-dn.net/?f=4x%20%3D%205)
![x = \frac{5}{4}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B5%7D%7B4%7D%20)
The x-intercept is
![( \frac{5}{4} , 0)](https://tex.z-dn.net/?f=%28%20%5Cfrac%7B5%7D%7B4%7D%20%2C%200%29)
To find the y-intercept,we substitute x=0 into the equation to get,
![4(0) + y = 5](https://tex.z-dn.net/?f=4%280%29%20%2B%20y%20%3D%205)
![y = 5](https://tex.z-dn.net/?f=y%20%3D%205)
The y-intercept is (0,5)
QUESTION 4.
The given equation is
![y = 5x - 4](https://tex.z-dn.net/?f=y%20%3D%205x%20-%204)
To find the y-intercept put x=0 into the equation.
![y = 5(0) - 4](https://tex.z-dn.net/?f=y%20%3D%205%280%29%20-%204)
![y = - 4](https://tex.z-dn.net/?f=y%20%3D%20%20-%204)
(0,-4)
To find the x-intercept, put y=0,
![0 = 5x - 4](https://tex.z-dn.net/?f=0%20%3D%205x%20-%204)
![4 = 5x](https://tex.z-dn.net/?f=4%20%3D%205x)
![\frac{4}{5} = x](https://tex.z-dn.net/?f=%20%5Cfrac%7B4%7D%7B5%7D%20%20%3D%20x)
![( \frac{4}{5} ,0)](https://tex.z-dn.net/?f=%28%20%5Cfrac%7B4%7D%7B5%7D%20%2C0%29)
QUESTION 5
To find the equation of a line given the slope m, and a point
![(x_1,y_1)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20)
we use the formula,
![y-y_1=m(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29)
The given line has slope zero and passes through
(3,4)
The equation is
![y - 4 = 0(x - 3)](https://tex.z-dn.net/?f=y%20-%204%20%3D%200%28x%20-%203%29)
![y - 4 = 0](https://tex.z-dn.net/?f=y%20-%204%20%3D%200)
![y = 4](https://tex.z-dn.net/?f=y%20%3D%204)
Question 6
The given equation is
![x = 1](https://tex.z-dn.net/?f=x%20%3D%201)
This is the equation of a line that is parallel to the y-axis.
The slope of all lines parallel to the x-axis is undefined.
The slope of x=1 is not defined.