Slope is a fundamental concept in algebra that describes the steepness and direction of a line. It is defined as the ratio of the vertical change (the rise) to the horizontal change (the run) between any two distinct points on a line. For a horizontal line, the rise is zero, resulting in a slope of zero. Conversely, a vertical line has a run of zero, which makes its slope undefined due to the impossibility of division by zero. By using the slope formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\), one can calculate the slope from given coordinates or identify it from a graph. Understanding these properties is essential for solving linear equations and analyzing the behavior of functions.
رقم الاختبار991
الصفالصف التاسع المتقدم
المادةرياضيات
الفصلالفصل الثالث
السنة الدراسية2025/2026
عدد الأسئلة10
إجمالي النقاط10
تاريخ الإضافة2026-04-23
الزيارات14
المعلم أو الناشرAmal Salman
اختر إجابة واحدة لكل سؤال. عند الاختيار ستظهر النتيجة فورًا: الأخضر صحيح، والأحمر خطأ، وسيظهر تفسير الإجابة مباشرة إن كان متوفرًا. وبعد آخر سؤال ستظهر الدرجة النهائية تلقائيًا.
Question 1
Points: 1
Determine the slope.
Explanation
By picking two points on the line, such as (1, 0) and (3, 5), the slope is calculated as \(m = \frac{5 - 0}{3 - 1} = \frac{5}{2}\).
Question 2
Points: 1
Identify the slope of the red line?
Explanation
The red line is horizontal. A horizontal line has no change in its y-coordinate (vertical change is 0), so its slope is always zero.
Question 3
Points: 1
m =
Explanation
Using points (0, -3) and (1, -1) from the graph, the slope is \(m = \frac{-1 - (-3)}{1 - 0} = \frac{2}{1} = 2\).
Question 4
Points: 1
Which line has a positive slope?
Explanation
A positive slope means the line rises from left to right. In the graph, the red line is the only one showing this upward trend.
Question 5
Points: 1
Which line has an undefined slope?
Explanation
Undefined slopes belong to vertical lines because the horizontal change (run) is zero. In the graph, the green line is vertical.
Question 6
Points: 1
Determine the slope between (4, 2) and (-3, 5).
Explanation
Using the formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\), we get \(m = \frac{5 - 2}{-3 - 4} = \frac{3}{-7} = -\frac{3}{7}\).
Question 7
Points: 1
Find the slope between (5, 2) and (3, 2).
Explanation
The y-coordinates are the same (2), meaning there is no vertical change (rise = 0). Therefore, the slope is 0.
Question 8
Points: 1
What is the slope of a horizontal line?
Explanation
A horizontal line has zero vertical change for any amount of horizontal change, which results in a slope of 0.
Question 9
Points: 1
Which of these is a solution to the equation y = 5x?
Explanation
If we substitute x = 1 into the equation, we get y = 5(1) = 5. Thus, (1, 5) satisfies the equation.
Question 10
Points: 1
Which of these is a solution to the equation y = 2x - 7?
Explanation
Substituting x = 2 into the equation results in y = 2(2) - 7 = 4 - 7 = -3. Therefore, (2, -3) is a solution.
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