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In the xy-coordinate system, if (r, s) and (r + 2, s +1) are two points on the line defined by the equation y = 4x + 5, then t =?
- a)4
- b)5
- c)8
- d)9
- e)11
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
In the xy-coordinate system, if (r, s) and (r + 2, s +1) are two point...
To solve this problem, you need to recognize that the slope of the line is equal to 4. In the standard equation for a line, y = mx + b, m is equivalent to the slope. The slope is equal to the change in y-values over the change in x-values; set up the following equation to solve for t:
slope = (s + t) − s/(r + 2) − r
4 = t /2
8 = t
slope = (s + t) − s/(r + 2) − r
4 = t /2
8 = t
Community Answer
In the xy-coordinate system, if (r, s) and (r + 2, s +1) are two point...
Given Information:
Two points on the line y = 4x + 5 are (r, s) and (r + 2, s + 1).
Equation of the Line:
The equation of the line is given as y = 4x + 5.
Using the Points:
Using the points (r, s) and (r + 2, s + 1) on the line, we can substitute these coordinates into the equation y = 4x + 5.
Substitute (r, s):
When we substitute the point (r, s) into the equation, we get s = 4r + 5.
Substitute (r + 2, s + 1):
When we substitute the point (r + 2, s + 1) into the equation, we get s + 1 = 4(r + 2) + 5.
Solve for t:
Now, we need to find the value of t, which is the difference between the y-coordinates of the two points.
t = (s + 1) - s
t = 4(r + 2) + 5 - (4r + 5)
t = 4r + 8 + 5 - 4r - 5
t = 8
Therefore, the value of t is 8, which corresponds to option (c).
Two points on the line y = 4x + 5 are (r, s) and (r + 2, s + 1).
Equation of the Line:
The equation of the line is given as y = 4x + 5.
Using the Points:
Using the points (r, s) and (r + 2, s + 1) on the line, we can substitute these coordinates into the equation y = 4x + 5.
Substitute (r, s):
When we substitute the point (r, s) into the equation, we get s = 4r + 5.
Substitute (r + 2, s + 1):
When we substitute the point (r + 2, s + 1) into the equation, we get s + 1 = 4(r + 2) + 5.
Solve for t:
Now, we need to find the value of t, which is the difference between the y-coordinates of the two points.
t = (s + 1) - s
t = 4(r + 2) + 5 - (4r + 5)
t = 4r + 8 + 5 - 4r - 5
t = 8
Therefore, the value of t is 8, which corresponds to option (c).
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In the xy-coordinate system, if (r, s) and (r + 2, s +1) are two points on the line defined by the equation y = 4x + 5, then t =?a)4b)5c)8d)9e)11Correct answer is option 'C'. Can you explain this answer?
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In the xy-coordinate system, if (r, s) and (r + 2, s +1) are two points on the line defined by the equation y = 4x + 5, then t =?a)4b)5c)8d)9e)11Correct answer is option 'C'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about In the xy-coordinate system, if (r, s) and (r + 2, s +1) are two points on the line defined by the equation y = 4x + 5, then t =?a)4b)5c)8d)9e)11Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the xy-coordinate system, if (r, s) and (r + 2, s +1) are two points on the line defined by the equation y = 4x + 5, then t =?a)4b)5c)8d)9e)11Correct answer is option 'C'. Can you explain this answer?.
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