Question

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Answer 1

QUESTION 1

We want to find the slope through the points (12,-18), (11,12).

We use the slope formula,

$m = \frac{y_2-y_1} {x _2-x_1}$

We substitute the points to get,

$m = \frac{12 - - 18}{11 - 12}$

$m = \frac{30}{ - 1} = - 30$

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,

$m = \frac{ - 15 - - 20}{ - 18 - - 18}$

We simplify to get;

$m = \frac{5}{0}$

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,

$4x + 0 = 5$

$4x = 5$

$x = \frac{5}{4}$

The x-intercept is

$( \frac{5}{4} , 0)$

To find the y-intercept,we substitute x=0 into the equation to get,

$4(0) + y = 5$

$y = 5$

The y-intercept is (0,5)

QUESTION 4.

The given equation is

$y = 5x - 4$

To find the y-intercept put x=0 into the equation.

$y = 5(0) - 4$

$y = - 4$

(0,-4)

To find the x-intercept, put y=0,

$0 = 5x - 4$

$4 = 5x$

$\frac{4}{5} = x$

$( \frac{4}{5} ,0)$

QUESTION 5

To find the equation of a line given the slope m, and a point

$(x_1,y_1)$

we use the formula,

$y-y_1=m(x-x_1)$

The given line has slope zero and passes through

(3,4)

The equation is

$y - 4 = 0(x - 3)$

$y - 4 = 0$

$y = 4$

Question 6

The given equation is

$x = 1$

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.