QUESTION 1
We want to find the slope through the points (12,-18), (11,12).
We use the slope formula,
[tex]m = \frac{y_2-y_1} {x _2-x_1} [/tex]
We substitute the points to get,
[tex]m = \frac{12 - - 18}{11 - 12} [/tex]
[tex]m = \frac{30}{ - 1} = - 30[/tex]
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,
[tex]m = \frac{ - 15 - - 20}{ - 18 - - 18} [/tex]
We simplify to get;
[tex]m = \frac{5}{0} [/tex]
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,
[tex]4x + 0 = 5[/tex]
[tex]4x = 5[/tex]
[tex]x = \frac{5}{4} [/tex]
The x-intercept is
[tex]( \frac{5}{4} , 0)[/tex]
To find the y-intercept,we substitute x=0 into the equation to get,
[tex]4(0) + y = 5[/tex]
[tex]y = 5[/tex]
The y-intercept is (0,5)
QUESTION 4.
The given equation is
[tex]y = 5x - 4[/tex]
To find the y-intercept put x=0 into the equation.
[tex]y = 5(0) - 4[/tex]
[tex]y = - 4[/tex]
(0,-4)
To find the x-intercept, put y=0,
[tex]0 = 5x - 4[/tex]
[tex]4 = 5x[/tex]
[tex] \frac{4}{5} = x[/tex]
[tex]( \frac{4}{5} ,0)[/tex]
QUESTION 5
To find the equation of a line given the slope m, and a point
[tex](x_1,y_1) [/tex]
we use the formula,
[tex]y-y_1=m(x-x_1)[/tex]
The given line has slope zero and passes through
(3,4)
The equation is
[tex]y - 4 = 0(x - 3)[/tex]
[tex]y - 4 = 0[/tex]
[tex]y = 4[/tex]
Question 6
The given equation is
[tex]x = 1[/tex]
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.
