Question

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

Answer 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 2

1 -
`y=-1`

2 -
`y=2x+4`

Explanation:

The general form of a straight line is
`y=mx+b`, 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,

`m=(2.5-2.5)/(4-0)=0`

Then, the y-intercept is given by,

`y=0x+b\\\\2.5=b`

That is, the equation of the line is
`y=2.5`

Since, 'Two parallel lines have equal slope'.

Then, the line parallel to
`y=2.5` have slope 0 i.e.
`y=b`.

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

Then, the equation of line is
`y=-1`

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,

`m=(-1-0)/(0+2)=(-1)/(2)`

Then, the y-intercept is given by,

`-1=(-1)/(2)* 0+b\\\\b=-1`

That is, the equation of the line is
`y=(-1)/(2)x-1`

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

Then, we have,

`m* (-1)/(2)=-1\\\\m=2`

The line perpendicular to
`y=(-1)/(2)x-1` have slope 2.

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

The y-intercept is given by,

`2=2* -1+b\\\\2=-2+b\\\\b=4`

Thus, the equation of the line is
`y=2x+4`

So, option A is correct.