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.

Ay = -1

By = 3

Cy = x -1

Dy = 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

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wagonbelleville wagonbelleville · Answer 2 · 2019-03-29T04:43:32-04:00

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.