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]
[tex]0=6x-18[/tex] or
[tex]6x=18[/tex]
⇒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]
[tex]y=6\cdot 0-18[/tex] or
[tex]y=-18[/tex]
⇒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 [tex]\frac{3}{4}[/tex]
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, [tex]\frac{3}{4}[/tex]
(B)
The slope of the original line is [tex]\frac{3}{4}[/tex].
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; [tex]-\frac{1}{m} = -\frac{4}{3}[/tex]
4.
The graph of the equation y =4x+5 as shown in figure 3
The x-intercept of this line is [tex]\frac{-5}{4}[/tex] = -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)
