[Math Revolution GMAT math practice question]
In the coordinate plane, the y-intercept of the line k is equal to twice its slope. The y-intercept is not 0. What is the x-intercept of the line k?
A. -2
B. -1
C. 0
D. 1
E. 2
In the coordinate plane, the y-intercept of the line k is eq
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- Max@Math Revolution
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$$k\,\,\,:\,\,\,y = ax + 2a\,\,\,\,\,\,\left( {a \ne 0} \right)\,\,\,\,\,\,\left( * \right)$$Max@Math Revolution wrote:[Math Revolution GMAT math practice question]
In the coordinate plane, the y-intercept of the line k is equal to twice its slope. The y-intercept is not 0. What is the x-intercept of the line k?
A. -2
B. -1
C. 0
D. 1
E. 2
$$?\,\,\,\,:\,\,\,{x_p}\,\,{\rm{when}}\,\,y = 0$$
$$\left( * \right)\,\,\,\, \Rightarrow \,\,\,\,\,\,0 = a\left( {{x_p} + 2} \right)\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{a \ne 0} \,\,\,\,\,\,\,? = {x_p} = - 2$$
This solution follows the notations and rationale taught in the GMATH method.
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One approach is to choose some values that meet the given information.Max@Math Revolution wrote:[Math Revolution GMAT math practice question]
In the coordinate plane, the y-intercept of the line k is equal to twice its slope. The y-intercept is not 0. What is the x-intercept of the line k?
A. -2
B. -1
C. 0
D. 1
E. 2
In the coordinate plane, the y-intercept of the line k is equal to twice its slope.
Okay, so let's say the y-intercept of line k is 6. We get:
Since the y-intercept (6) is TWICE the slope, we know that the slope = 3
What is the x-intercept of the line k?
Since (x, 0) are the coordinates of the x-intercept . . .
. . . we can apply the slope formula to wrote: (6 - 0)/(0 - x) = 3
Simplify: 6/(-x) = 3
Multiply both sides by -x to get: 6 = -3x
Solve: x = 6/(-3) = -2
Answer: A
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Brent
- Max@Math Revolution
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=>
The equation of line k has the form, y = mx + b, where m is the slope and b is the y-intercept.
Let m be the slope of line k. Then b = 2m, and the equation is y = mx + 2m = m(x+2).
The x-intercept of line k is -2, since -2 is a root of m(x+2)=0.
Therefore, the answer is A.
Answer: A
The equation of line k has the form, y = mx + b, where m is the slope and b is the y-intercept.
Let m be the slope of line k. Then b = 2m, and the equation is y = mx + 2m = m(x+2).
The x-intercept of line k is -2, since -2 is a root of m(x+2)=0.
Therefore, the answer is A.
Answer: A
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We can let m = the slope, and thus 2m = the y-intercept. The equation of the line isMax@Math Revolution wrote:[Math Revolution GMAT math practice question]
In the coordinate plane, the y-intercept of the line k is equal to twice its slope. The y-intercept is not 0. What is the x-intercept of the line k?
A. -2
B. -1
C. 0
D. 1
E. 2
y = mx + 2m
To find the x-intercept, we set y = 0 and solve for x. Thus, we have:
0 = mx + 2m
-mx = 2m
Since the y-intercept is non-zero, m is non-zero as well. Thus, we can divide each side by -m:
x = 2m/(-m)
x = 2/(-1) = -2
Answer: A
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