Examples with solutions for Graphical Representation: Determining the slope of a function with a point

Exercise #1

A straight line has a slope of 6y and passes through the points (6,41) (6,41) .

Which function corresponds to the line described?

Video Solution

Step-by-Step Solution

To solve the exercise, we will start by inserting the available data into the equation of the line:
y = mx + b
41 = 6*6 + b
41 = 36 +b
41-36 = b
5 = b
 
Now we have the data for the equation of the straight line:
 
y = 6x + 5
But it still does not match any of the given options.

Keep in mind that a common factor can be excluded:
y = 2(3x + 2.5)

Answer

y=2(3x+212) y=2(3x+2\frac{1}{2})

Exercise #2

A straight line with a slope of 2y passes through the point (3,7) (3,7) .

Which equation corresponds to the line?

Video Solution

Answer

y=2x+1 y=2x+1

Exercise #3

A straight line with the slope 9y passes through the point (5,8) (-5,-8) .

Which of the following equations corresponds to the line?

Video Solution

Answer

y=9x+37 y=9x+37

Exercise #4

Given the line parallel to the line y=2x+5 y=2x+5

and passes through the point (4,9) (4,9) .

Which of the algebraic representations is the corresponding one for the given line?

Video Solution

Answer

y=2x+1 y=2x+1

Exercise #5

Given the line parallel to the line y=3x+4 y=3x+4

and passes through the point (12,1) (\frac{1}{2},1) .

Which of the algebraic representations is the corresponding one for the given line?

Video Solution

Answer

y=3x12 y=3x-\frac{1}{2}

Exercise #6

Given the line parallel to the line y=4 y=4

and passes through the point (1,2) (1,2) .

Which of the algebraic representations is the corresponding one for the given line?

Video Solution

Answer

y=2 y=2

Exercise #7

A line has a slope of 12 \frac{1}{2} and passes through the point (5,1712) (5,17\frac{1}{2}) .

Which expression corresponds to the line?

Video Solution

Answer

y=12x+15 y=\frac{1}{2}x+15

Exercise #8

Given the line parallel to the line y=2x5 y=2x-5

and passes through the point (3,4) (-3,-4) .

Which of the algebraic representations is the corresponding one for the given line?

Video Solution

Answer

y=2x+2 y=2x+2

Exercise #9

A line has a slope of 112 1\frac{1}{2} and passes through the point (3,712) (3,7\frac{1}{2}) .

Which expression corresponds to the line?

Video Solution

Answer

y=112(x+2) y=1\frac{1}{2}(x+2)

Exercise #10

A straight line with a slope of 2y passes through the point (7,11) (7,11) .

Which expression corresponds to the line?

Video Solution

Answer

y=3x3x y=3x-3-x

Exercise #11

Given the line parallel to the line

y=34x+2 y=-\frac{3}{4}x+2

and passes through the point (8,2) (8,2) .

Which of the algebraic representations is the corresponding one for the given line?

Video Solution

Answer

y=34x+8 y=-\frac{3}{4}x+8