Question

1.Graph the equation y = 6x -18:

Answer 1

Answer:

1. Given the equation: y =6x-18                        ......[1]

The intercepts of a line are the points where the line intercepts or crosses the horizontal and vertical axes.

(A)

Horizontal intercept(x) states that the point where the line crosses the x-axis and at this point y=0

Put y=0 in equation [1]

$0=6x-18$ or

$6x=18$

⇒x=3

Ordered pair of horizontal intercept(x) = (3,0)

(B)

Vertical intercept(y) states that the point where the line crosses the y-axis and at this point x=0.

Put x=0 in equation [1]

$y=6\cdot 0-18$ or

$y=-18$

⇒y=-18

Ordered pair of vertical intercept(y) = (0,-18)

You can also see the graph  of the function y =6x-18 as shown in Figure-1.

2.

Graph the equation y+2x =4

to find the horizontal intercept and vertical intercept we follow the same process as done in 1

(A)

Horizontal intercept (x) = 2

Ordered pair = (2,0)

(B)

Vertical intercept (y) = 4

Ordered pair = (0,4)

Also, you can see these in the graph as shown in the Figure-2

3.

Given: The slope(m) of a line is $\frac{3}{4}$

Two lines are parallel if their slopes are equal and they have different y - intercepts.

(A).

The slope of a line parallel to it is, $\frac{3}{4}$

(B)

The slope of the original line is  $\frac{3}{4}$.

A line perpendicular to another line  has a slope that is the negative reciprocal of the slope of the other line.

Therefore, slope of a line perpendicular to it is; $-\frac{1}{m} = -\frac{4}{3}$

4.

The graph of the equation y =4x+5 as shown in figure 3

The x-intercept of this line is $\frac{-5}{4}$ = -1.25

And the y-intercept of this line is y =5.

5.

Graph of the equation y = -3 represents the line as shown in figure 4.

6.

Solve the equation:

6y-18x = -18

6y = 18x-18

Divide by 6 to both sides of an equation ; we get

y = 3x-3 or

y = 3(x-1)