Question

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

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

Answer:

1 - $y=-1$

2 - $y=2x+4$

Step-by-step 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,

$m=\frac{2.5-2.5}{4-0}=0$

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,

$m=\frac{-1-0}{0+2}=\frac{-1}{2}$

Then, the y-intercept is given by,

$-1=\frac{-1}{2}\times 0+b\\\\b=-1$

That is, the equation of the line is $y=\frac{-1}{2}x-1$

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

Then, we have,

$m\times \frac{-1}{2}=-1\\\\m=2$

The line perpendicular to $y=\frac{-1}{2}x-1$ have slope 2.

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

The y-intercept is given by,

$2=2\times -1+b\\\\2=-2+b\\\\b=4$

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

So, option A is correct.