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 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.
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.
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