In math class, students must randomly draw a card that contains an equation that they must graph on the board.
If the cards contain the equations 2y = 4x + 2, x(x + 1) = 0, 2x + y = 0, x = 2y , x2 + 1 = 0, and y - 2x = 0, then what is the probability that a student will graph a line whose slope is 2?
I see 6 equations.
Of those only one has a slope of 2
mmmhhh?
To determine the probability that a student will graph a line whose slope is 2, we need to find the number of equations with a slope of 2 and divide it by the total number of equations given.
Let's analyze each equation one by one, checking if they have a slope of 2:
1. 2y = 4x + 2
This equation can be rewritten in slope-intercept form as y = 2x + 1.
The slope of this line is 2, so it satisfies the condition.
2. x(x + 1) = 0
This equation is not in slope-intercept form, but we can solve it to find the slope.
By factoring, we get x(x + 1) = 0 → x = 0 or x = -1.
Neither solution has a slope of 2, so it does not satisfy the condition.
3. 2x + y = 0
Rewriting this equation in slope-intercept form, we have y = -2x.
The slope of this line is -2, not 2.
4. x = 2y
This equation can be rewritten as y = (1/2)x.
The slope is 1/2, not 2.
5. x^2 + 1 = 0
This equation is not linear and cannot be graphed as a line, so it is not relevant to our calculation.
6. y - 2x = 0
Rewriting this equation in slope-intercept form, we have y = 2x.
The slope of this line is 2, so it satisfies the condition.
Out of the six equations, two of them have a slope of 2: 2y = 4x + 2 and y - 2x = 0.
Therefore, the probability that a student will graph a line whose slope is 2 is 2/6, which simplifies to 1/3 or approximately 0.333.
To determine the probability that a student will graph a line whose slope is 2, we need to find out how many cards contain equations representing lines with a slope of 2, and then calculate the ratio between the number of favorable outcomes and the total number of possible outcomes.
Let's analyze each equation and determine if it represents a line with a slope of 2:
1. 2y = 4x + 2
Divide both sides of the equation by 2 to put it in slope-intercept form: y = 2x + 1
The slope of this line is 2.
2. x(x + 1) = 0
This equation is quadratic, not linear. It does not represent a line with a slope of 2.
3. 2x + y = 0
Rearranging the equation to slope-intercept form: y = -2x
The slope of this line is -2, not 2.
4. x = 2y
Rearranging the equation to slope-intercept form: y = (1/2)x
The slope of this line is 1/2, not 2.
5. x^2 + 1 = 0
This equation is also quadratic, not linear. It does not represent a line with a slope of 2.
6. y - 2x = 0
Rearranging the equation to slope-intercept form: y = 2x
The slope of this line is 2.
Out of the six given equations, only two represent lines with a slope of 2: 2y = 4x + 2 and y - 2x = 0.
Therefore, the favorable outcomes are 2.
The total number of possible outcomes is 6 since there are six cards containing equations.
So, the probability that a student will randomly draw a card with an equation representing a line whose slope is 2 is 2/6 = 1/3, or approximately 0.3333.