Interactive multiple-choice quiz: Creating Linear Equations ريفيل
This document contains exercises on finding the y-intercept and writing the equation of a line using the slope-intercept form $y = mx + b$. These problems help students practice substituting points and slopes into the linear equation formula to derive the complete equation of a line.
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اختبار شهادة تدريبي مؤقت للصف والمادة والفصل نفسه.
اختر إجابة لكل سؤال لتظهر النتيجة والتفسير فورًا، وتظهر درجتك بعد الانتهاء. الأسئلة من إعداد المدرس، أما الإجابات فحُدّدت بالذكاء الاصطناعي وقد تحتمل الخطأ؛ يمكنك الإبلاغ عبر أيقونة العلم بجانب السؤال.
Using the slope-intercept form y = mx + b, find the value of b for the line that passes through (-8, 6) with a slope of $m = -\frac{3}{4}$
Explanation
Substitute the point (-8, 6) and the slope $m = -\frac{3}{4}$ into the slope-intercept equation y = mx + b. This gives $6 = -\frac{3}{4}(-8) + b$, which simplifies to 6 = 6 + b. Subtracting 6 from both sides, we find b = 0.
Write the final equation of the line in slope-intercept form using the slope $m = -\frac{3}{4}$ and the y-intercept b = 0
Explanation
The slope-intercept form is y = mx + b. Plugging in the given values $m = -\frac{3}{4}$ and b = 0, the equation becomes $y = -\frac{3}{4}x + 0$, which simplifies to $y = -\frac{3}{4}x$.
The total monthly cost of Ayzha's gym membership increases by 5 per class she attends. After signing up for 4 classes one month, her total cost is49.99. Which equation represents Ayzha's total monthly cost y after attending x classes?
Explanation
The slope is 5. Substitute (4, 49.99) into y = 5x + b: b = 49.99 - 20 = 29.99, so y = 5x + 29.99.
The table shows the number of students enrolled in public high schools in the United States since 2010. Which linear equation best represents the data if x represents the number of years since 2010?
Explanation
Using the first and last table entries, the average rate is (14912 - 14749)/(2015 - 2011) = 40.75 thousand students per year. Since 2011 corresponds to x = 1, b = 14749 - 40.75 = 14708.25. This is an approximate endpoint model, not an exact fit to every row.
Question 6
6
Points: 10
Write an equation of the line that passes through (4, 2) and has slope 1/2.
Explanation
With m = 1/2, b = 2 - (1/2)(4) = 0, so y = (1/2)x.
The provided table details the relationship between distance and total fare cost for taxi rides, where x denotes distance in miles and y denotes cost in dollars. Which of the following equations correctly represent the situation in point-slope form? A: y - 13.4 = 2.6(x - 4); B: y - 22.5 = 2.6(x - 7.5); C: y = 2.6x + 3; D: y - 6.9 = (5/13)(x - 1.5); F: y + 34.85 = 2.6(x + 12.25). Select the correct group.
Explanation
The rate is (13.40 - 6.90)/(4 - 1.5) = 2.6 dollars per mile. A and B use this slope and points from the table. C represents the same line but is in slope-intercept form, not point-slope form. D has the wrong slope; F has incorrect signs.
Question 15
15
Points: 10
Write y = -(7/2)x + 5 in standard form Ax + By = C, using integer coefficients with A > 0.
Explanation
Multiply by 2: 2y = -7x + 10. Move 7x to the left: 7x + 2y = 10. The equivalent equation in B is excluded by the stated positive-A convention.
Select the equation in slope-intercept form for the line that passes through (5, 0) and is perpendicular to the graph of x - 6y = 1.
Explanation
The given line has slope 1/6, so the perpendicular slope is -6. Passing through (5, 0) gives b = 30. A is in the requested slope-intercept form; B is equivalent but is in standard form.
Find the inverse of the relation shown in the table.
Explanation
The original pairs are (-11, 9), (0.3, -2), (-3, -8) and (3.5, 2). Swapping their coordinates gives {(9, -11), (-2, 0.3), (-8, -3), (2, 3.5)}.
Question 28
28
Points: 10
Graph the inverse of the relation. The graph of the relation passes through the points (-1, -5), (0, -2), (1, 1), and (2, 4). Which set of points represents the inverse relation?
Explanation
Swap the coordinates of each original point: (-1, -5) becomes (-5, -1), (0, -2) becomes (-2, 0), (1, 1) stays (1, 1), and (2, 4) becomes (4, 2).
Question 29
29
Points: 10
Find the inverse of f(x) = 5x + 10.
Explanation
Replace f(x) with y, swap x and y, then solve: x = 5y + 10 gives y = (x - 10)/5 = (1/5)x - 2.
CANDLES: Javi is making candles to sell at an upcoming festival. He has already made 38 candles, and he makes 24 candles each day. The function C(x) = 24x + 38 represents the total number of candles in inventory, where x is the number of days since he began making more candles. Part A: Select the inverse of C(x) = 24x + 38.
Explanation
Swap x and y and solve: x = 24y + 38 gives y = (x - 38)/24 = (1/24)x - 19/12.
Here are more quizzes for الصف التاسع المتقدم by الفصل الأول and subject رياضيات
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