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The notion of line or straight line is to represent straight objects in geometry. Lines are an idealization of such objects, often described in terms of two points. Take this quiz to test your knowledge and clear your concepts about straight lines. Read the questions carefully and answer.
Questions and Answers
1.
A.
Function
B.
Non-Function
Correct Answer B. Non-Function
Explanation The x-value -1 has two y-values 7 and 8.
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2.
Find the slope through the points (4, -2) and (-1, 6).
A.
-5/8
B.
8/5
C.
-8/5
D.
-3
Correct Answer C. -8/5
Explanation To find the slope between two points, we use the formula (y2 - y1) / (x2 - x1). In this case, the coordinates of the first point are (4, -2) and the coordinates of the second point are (-1, 6). Plugging these values into the formula, we get (6 - (-2)) / (-1 - 4), which simplifies to 8 / -5. Therefore, the slope between these two points is -8/5.
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3.
Find the slope of the linear equation:
A.
2
B.
-1/2
C.
-6
D.
-2
Correct Answer D. -2
Explanation The slope of a linear equation is the coefficient of the variable x. In this case, the coefficient of x is -2, which means that for every unit increase in x, the y-value decreases by 2 units.
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4.
Write the equation of the line given slope of 5 and y-intercept of -2.
A.
Y = 5x - 2
B.
Y = -2x + 5
C.
Y = 5x + 2
D.
5x - 2y = 3
Correct Answer A. Y = 5x - 2
Explanation The equation of a line can be written in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is given as 5 and the y-intercept is -2. Therefore, the equation of the line is y = 5x - 2.
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5.
Write the equation of a line with slope and through the point (9, -3).
A.
Y = 2/3 x - 6
B.
Y = 2/3 x - 9
C.
Y = 2/3 x - 3
D.
Y = 2/3 x + 3
Correct Answer B. Y = 2/3 x - 9
Explanation The equation of a line can be written in the form y = mx + b, where m is the slope and b is the y-intercept. In this question, the slope is given as 2/3 and the line passes through the point (9, -3). To find the y-intercept, we substitute the values of x and y from the given point into the equation and solve for b. Plugging in x = 9 and y = -3, we get -3 = (2/3)(9) + b. Simplifying this equation gives b = -9. Therefore, the equation of the line is y = 2/3 x - 9.
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6.
When a function is in slope-intercept form (y=mx+b), what does b stand for?
A.
The slope
B.
The Y-intercept
C.
The X-intercept
D.
The Z-intercept
E.
Half of the initial value
Correct Answer B. The Y-intercept
Explanation In the slope-intercept form, y=mx+b, the variable b represents the y-intercept. The y-intercept is the point where the graph of the function intersects the y-axis. It indicates the value of y when x is equal to zero. So, in this case, b represents the initial value or the value of y when x=0.
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7.
What is the formula for slope?
A.
Rise over run
B.
Run over rise
C.
X over Y
D.
Y-intercept times X-intercept divided by pie
E.
The opposite of the X-intercept
Correct Answer A. Rise over run
Explanation The formula for slope is rise over run. This means that to calculate the slope, you divide the change in the y-values (rise) by the change in the x-values (run). It represents the steepness or incline of a line on a graph.
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8.
What is '2x+3y=18' in slope intercept form?
A.
Y=-2x+18
B.
Y=-(2/3)x+18
C.
Y=-(2/3)x+6
D.
Y=2x+6
E.
Y=(2/3)x+18
Correct Answer C. Y=-(2/3)x+6
Explanation The equation 2x+3y=18 can be rearranged into slope-intercept form, which is y=mx+b, where m represents the slope and b represents the y-intercept. In this case, the correct answer is y=-(2/3)x+6, which means that the slope is -(2/3) and the y-intercept is 6.
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9.
The form of a function that is written as ax+by=c is __________ form.
Correct Answer standard
Explanation The form of a function that is written as ax+by=c is called the standard form. In this form, the coefficients a, b, and c represent the constants in the equation. The variables x and y represent the independent and dependent variables, respectively. The standard form is commonly used in mathematics to represent linear equations and is useful for solving systems of equations and finding the x and y-intercepts.
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10.
According to the video, what are the steps to graphing a linear equation? (Make sure your sound is on.)
A.
Graph the slope, graph the y-intercept, then connect them.
B.
Solve for y, plot the slope, plot the y-intercept.
C.
Solve for y by isolating it, identify slope and y-int, plot the y-int, use the slope to plot another point then draw line through the points.
D.
Put equation in standard form, find two points, draw a line through them.
Correct Answer C. Solve for y by isolating it, identify slope and y-int, plot the y-int, use the slope to plot another point then draw line through the points.
Explanation The correct answer explains the steps to graphing a linear equation in a clear and logical manner. It starts by solving for y by isolating it, which allows us to identify the slope and y-intercept. Then, we plot the y-intercept on the graph and use the slope to plot another point. Finally, we connect the two points with a line to graph the linear equation. This answer provides a comprehensive and accurate explanation of the process.
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11.
2x - y = 6Find the y-intercept of the line.
A.
-2
B.
-6
C.
6
D.
-3
Correct Answer B. -6
Explanation To find the y-intercept of a line, we need to set the value of x to 0 and solve for y. In the given equation, when x is 0, we have 2(0) - y = 6, which simplifies to -y = 6. By multiplying both sides of the equation by -1, we get y = -6. Therefore, the y-intercept of the line is -6.
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12.
Is the point (1,1) on the line y = 2x + 1?
A.
Yes
B.
No
C.
Sometimes
Correct Answer B. No
Explanation The point (1,1) is not on the line y = 2x + 1 because when we substitute x = 1 into the equation, we get y = 2(1) + 1 = 3, which is not equal to 1. Therefore, the point (1,1) does not satisfy the equation and is not on the line.
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13.
2x + 4y = 8x + 2y = 6The slopes of these two lines are:
A.
Parallel
B.
Perpendicular
C.
Neither
D.
Intersecting
Correct Answer A. Parallel
Explanation The given equation represents two lines in the form of 2x + 4y = 8x + 2y = 6. By simplifying the equation, we can rewrite it as 2x + 4y = 6 and 8x + 2y = 6. The slopes of these lines can be determined by rearranging the equations in slope-intercept form (y = mx + b), where m represents the slope. The first equation can be rewritten as y = -0.5x + 1.5, and the second equation can be rewritten as y = -4x + 3. Comparing the slopes, we can see that they are both different (-0.5 and -4), indicating that the lines are not parallel, perpendicular, or intersecting. Therefore, the correct answer is "Neither".
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14.
Which point is a solution to the line 2y = -8 + 3x?
A.
(0,0)
B.
(1,4)
C.
(3,2)
D.
(4,2)
Correct Answer D. (4,2)
Explanation The given equation is in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. In this case, the equation is 2y = -8 + 3x, which can be rewritten as y = (3/2)x - 4. By substituting the x and y values of each point into the equation, we can determine if it satisfies the equation. Only the point (4,2) satisfies the equation, making it the solution.
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15.
Given: f(x) = 3x - 2
Find f(0)
A.
-2
B.
-1
C.
0
D.
2
Correct Answer A. -2
Explanation substitute in zero for x and evaluate the right side of the equation
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16.
If two line contain the same slope and different y-intercepts, then:
A.
The lines intersect at one point.
B.
The lines will never intersect.
C.
The lines intersect at all point.
Correct Answer B. The lines will never intersect.
Explanation If two lines have the same slope and different y-intercepts, it means that they are parallel to each other. Parallel lines never intersect, as they maintain a constant distance between them at all points. Therefore, the correct answer is that the lines will never intersect.