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When graphed in the xy-plane, the line y = mx - 4 intersects t he x-a x is at an angle of θ. If m > 0, 0° < θ < 90°, and cos θ = 3/√58, what is the value of m?
Correct answer is '2.33'. Can you explain this answer?
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When graphed in the xy-plane, the line y = mx - 4 intersects t he x-a ...
The graph of the line y = mx - 4 has a slope of m and a y-intercept of -4. Since m > 0, this slope is positive. We are told that this line intersects the x-axis at an angle of θ, where cos θ = 3/√58. This gives us enough information to sketch a fairly detailed graph:
Notice that this information lets us construct a right triangle that includes θ, in which the adjacent side has length 3 and the hypotenuse has length √58 (remember cos θ = adjacent/hypotenuse). This triangle is particularly handy because it depicts the rise and the run for a portion of the line, which will enable us to find the slope. We simply have to find the rise with the
Pythagorean Theorem: 32 + rise2 = (√58)
Simplify: 9 + rise2 = 58
Subtract 9: rise2 = 49
Take square root: rise = 7
Therefore, the slope of the line is m = rise/run = 7/3 or 2.33
Notice that this information lets us construct a right triangle that includes θ, in which the adjacent side has length 3 and the hypotenuse has length √58 (remember cos θ = adjacent/hypotenuse). This triangle is particularly handy because it depicts the rise and the run for a portion of the line, which will enable us to find the slope. We simply have to find the rise with the
Pythagorean Theorem: 32 + rise2 = (√58)
Simplify: 9 + rise2 = 58
Subtract 9: rise2 = 49
Take square root: rise = 7
Therefore, the slope of the line is m = rise/run = 7/3 or 2.33
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When graphed in the xy-plane, the line y = mx - 4 intersects t he x-a x is at an angle of θ. If m > 0, 0° < θ < 90°, and cos θ = 3/√58, what is the valueof m?Correct answer is '2.33'. Can you explain this answer?
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When graphed in the xy-plane, the line y = mx - 4 intersects t he x-a x is at an angle of θ. If m > 0, 0° < θ < 90°, and cos θ = 3/√58, what is the valueof m?Correct answer is '2.33'. Can you explain this answer? for SAT 2025 is part of SAT preparation. The Question and answers have been prepared according to the SAT exam syllabus. Information about When graphed in the xy-plane, the line y = mx - 4 intersects t he x-a x is at an angle of θ. If m > 0, 0° < θ < 90°, and cos θ = 3/√58, what is the valueof m?Correct answer is '2.33'. Can you explain this answer? covers all topics & solutions for SAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When graphed in the xy-plane, the line y = mx - 4 intersects t he x-a x is at an angle of θ. If m > 0, 0° < θ < 90°, and cos θ = 3/√58, what is the valueof m?Correct answer is '2.33'. Can you explain this answer?.
When graphed in the xy-plane, the line y = mx - 4 intersects t he x-a x is at an angle of θ. If m > 0, 0° < θ < 90°, and cos θ = 3/√58, what is the valueof m?Correct answer is '2.33'. Can you explain this answer? for SAT 2025 is part of SAT preparation. The Question and answers have been prepared according to the SAT exam syllabus. Information about When graphed in the xy-plane, the line y = mx - 4 intersects t he x-a x is at an angle of θ. If m > 0, 0° < θ < 90°, and cos θ = 3/√58, what is the valueof m?Correct answer is '2.33'. Can you explain this answer? covers all topics & solutions for SAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When graphed in the xy-plane, the line y = mx - 4 intersects t he x-a x is at an angle of θ. If m > 0, 0° < θ < 90°, and cos θ = 3/√58, what is the valueof m?Correct answer is '2.33'. Can you explain this answer?.
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When graphed in the xy-plane, the line y = mx - 4 intersects t he x-a x is at an angle of θ. If m > 0, 0° < θ < 90°, and cos θ = 3/√58, what is the valueof m?Correct answer is '2.33'. Can you explain this answer?, a detailed solution for When graphed in the xy-plane, the line y = mx - 4 intersects t he x-a x is at an angle of θ. If m > 0, 0° < θ < 90°, and cos θ = 3/√58, what is the valueof m?Correct answer is '2.33'. Can you explain this answer? has been provided alongside types of When graphed in the xy-plane, the line y = mx - 4 intersects t he x-a x is at an angle of θ. If m > 0, 0° < θ < 90°, and cos θ = 3/√58, what is the valueof m?Correct answer is '2.33'. Can you explain this answer? theory, EduRev gives you an
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