Graph with a line going through points zero comma two point five and four comma two point five.

Select the equation of the line that passes through the point (3, -1) and is parallel to the line on the graph.

a) y = -1

b) y = 3

c) y = x -1

d) y = 3x - 1
graph is attached for 1st question

Graph with a line going through points negative 2 comma zero and 0 comma negative one.

Select the equation of a line that is perpendicular to the line on the graph and passes through the point (-1, 2).

y = 2x + 4

y = - 2x + 2

y = - 1 over 2 x + 2

y = 2x - 1

y= - 1

The graph of the first line is 0. The graph of the second line will also be equal to 0. Replacing in the general equation of a line y=mx+c;
y=(0)x+c
y=c
Using the point (3,-1)
-1=c
y=-1

Answer Link

wagonbelleville wagonbelleville · Answer 2 · 2019-03-29T09:43:32+01:00

Answer:

1 - [tex]y=-1[/tex]

2 - [tex]y=2x+4[/tex]

Step-by-step explanation:

The general form of a straight line is [tex]y=mx+b[/tex], where m = slope and b = y-intercept.

Ques 1: We are given that the line passes through (0,2.5) and (4,2.5).

Then the slope of the line is given by,

[tex]m=\frac{2.5-2.5}{4-0}=0[/tex]

Then, the y-intercept is given by,

[tex]y=0x+b\\\\2.5=b[/tex]

That is, the equation of the line is [tex]y=2.5[/tex]

Since, 'Two parallel lines have equal slope'.

Then, the line parallel to [tex]y=2.5[/tex] have slope 0 i.e. [tex]y=b[/tex].

As, the line passes through the point (3,-1) i.e. y= -1 for any value of x.

Then, the equation of line is [tex]y=-1[/tex]

So, option A is correct.

Ques 2: We are given that the line passes through (-2,0) and (0,-1).

Then the slope of the line is given by,

[tex]m=\frac{-1-0}{0+2}=\frac{-1}{2}[/tex]

Then, the y-intercept is given by,

[tex]-1=\frac{-1}{2}\times 0+b\\\\b=-1[/tex]

That is, the equation of the line is [tex]y=\frac{-1}{2}x-1[/tex]

Since, 'The product of slopes of two perpendicular lines is -1'.

Then, we have,

[tex]m\times \frac{-1}{2}=-1\\\\m=2[/tex]

The line perpendicular to [tex]y=\frac{-1}{2}x-1[/tex] have slope 2.

As, the line passes through the point (-1,2) with slope 2.

The y-intercept is given by,

[tex]2=2\times -1+b\\\\2=-2+b\\\\b=4[/tex]

Thus, the equation of the line is [tex]y=2x+4[/tex]

So, option A is correct.