# Graphs, Equation of Line, Midpoints and Line Segments

Please see the attached file for the fully formatted problems.

1.) Find the distance between the points (4,-1) and (-5,3)

2.) Find the midpoint of the line segment with endpoints (5,-2) and (-3,12)

3.) Graph the equation

4.)

5.) Find the equation of the line with slope 0 and y-intercept (0,-2). Write your answer in the form y=mx+b

6.) Write the equation of the line passing through (5,2) and (4,-2)

7.) Find the vertex of the graph of the parabola f(x)=-

8.)

9.)

10.)

11.)

12.)

3x+2if x find f(-1)

13.) Which set of ordered pairs (x,y) define y as a function of x?

I.)

II.) {(5,1), (-3,4), (-3,2)}

14.) Determine the domain of the function f(x) =

15.) Consider all the ordered pairs shown on Graph A and all the ordered pairs shown on Graph B. Which set of ordered pairs defines a function?

16.) The length of the base of a triangle is eight times the length of its altitude. Express the area (A) of the triangle as a function of its altitude x.

17.) Find the slope of the line passing through the points (-1,-2) and (1,4)

18.)

For any two parallel lines:

A.

the slopes are zero

B.

the slopes are reciprocals

C.

the slopes are positive

D.

the slopes are equal

19.) Find the value of x in the domain of f(x)=-2x-3 for which f(x)=3

20.) If the quadratic function f(x)= -4x+6 is graphed the range has

A.) a maximum value

B.

a minimum value

C.

no maximum or minimum value

D.

many maximum and minimum values.

https://brainmass.com/math/graphs-and-functions/graphs-equation-line-midpoints-line-segments-213890

#### Solution Preview

Please see the attached file for the complete solution.

1.) Find the distance between the points (4,-1) and (-5,3)

D = SQRT ((X2 - X1)2 + (Y2 - Y1)2)

= SQRT (81 + 16)

= SQRT (97)

= 17.5

2.) Find the midpoint of the line segment with endpoints (5,-2) and (-3,12)

MIDx = (X2 - X1)/2

= (-3 - 5)/2

= -4

MIDy = (Y2 - Y1)/2

= (12 + 2)/2

= 7

MID point is (-4, 7)

3.) Graph the equation

4.)

5.) Find the equation of the line with slope 0 and y-intercept (0,-2). Write your answer in the form y=mx+b

Slope 0 means m = 0 therefore

Y = b

y-intercept (0,-2) means b = -2, therefore:

y = -2

6.) Write the equation of the line passing through ...

#### Solution Summary

Twenty graphs, equation of line, ,midpoints and line segments related questions are answered.