Question

Suppose we are given the following information.

Answer 1

Answer: perpendicular

Step-by-step explanation: Line 1 has the following points

(-2,5) and (1,4)

We know that the equation of a straight has the form

y=mx+c

m=gradient or the slope

c= where the graph crosses the y axis

let us label our points

let(x1, y1)=(-2, -5)

let (x2, y2)=(1, 4)

Does not matter the labelling of points

we now need to find the gradient or the slope

It is given by the following formula

m=(y2-y1)/(x2-x1)

substitute the values into formula

m=(4--5)/(1--5)=9/3=3

Reminder that two negatives facing each other gives a postive

m=3

We substitute this into our general equation of a straight line to get the following:

y=3x+c

We now to solve for c

and we can use any of the two co-ordinate points

lets use(1,4) this means x=1 and y=4

substitute into the above equations and solve for c

4=3*1+c

4=3+c

c=1

the equation for Line1 is y=3x+1

We now look at line2

(0,6) and (6,4)

let(x1, y1)=(0,6) and (x2, y2)=(6,4)

We following the same procedure as for the first line

we look for the gradient or slope m

m=(y2-y1)/x2-x1)

m=(4-6)/(6-0)=-2/6=-1/3

We then substitute this value into the general equation for a line

y=mx+c

y=-1/3x+c

we now need to solve for c

we can choose any of the co-ordinate points to substitute into the equation

say we choose(0,6) this means x=0 and y=6

y=-1/3x+c

6=-1/3 *0+c

6=0+c

c=6

we then get the equation for line 2 which is

y=-1/3x+6

Line 1 has a gradient of 3

Line2 has a gradient of -1/3

when we multiply the two together we get -1

therefore the two line are perpendicular to each other

m1*m2=-1

gradient of line multiplied by the gradient of line 2 gives -1

perpendicular line

Answer 2

Answer: the lines are neither parallel nor perpendicular.

To determine whether two lines are parallel, perpendicular, or neither, we need to calculate their slopes. The slope of a line is a measure of how steep the line is. It is calculated by dividing the difference in the y-coordinates of the two points by the difference in the x-coordinates.

For line 1, the slope is calculated as follows: (4-(-5))/(1-(-2)) = 9/3.

For line 2, the slope is calculated as follows: (4-6)/(6-0) = -2/6 = -1/3.

Since the slopes of the two lines are different, they are not parallel.

To determine whether two lines are perpendicular, we need to check if the product of their slopes is -1. The product of the slopes of line 1 and line 2 is (9/3)*(-1/3) = -3/9 = -1/3. Since this is not equal to -1, the lines are not perpendicular.

Therefore, the lines are neither parallel nor perpendicular.