- A First, determine the equation for the line. Since the slope is^23 , the equation
initially reads: y =^23 x + b. To solve for b, substitute the coordinates (6,14) into
the equation:
y =^23 x + b
14 =^23 (6) + b
14 = 4 + b
b = 10
The equation for the line is thus y =^23 x + 10. Since the x-intercept represents
the point at which the line intersects the x-axis, the y-coordinate of that
point will be zero. Thus substitute 0 for y into the equation to determine the
x-intercept:
0 =^23 x + 10
−10 =^23 x
−10 (^32 ) = x
−15 = x - D Draw the diagram and connect the points (0,0) and (−5,5). The resulting
line will be the hypotenuse of a right triangle whose legs each have a length
of 5.
(–5, 5)^525√ 5Since this is an isosceles right triangle, the hypotenuse will be 5√ 2.- B and D Any line with a negative slope will intercept quadrants II and IV.
Whether the line intercepts Quadrant I or III depends on the line’s y-intercept.
Since you are not given information about the line’s y-intercept, you cannot
determine whether it will pass through the other quadrants or the origin. The
correct answer is II and IV. For illustration, see the following figure:
444 PART 4 ■ MATH REVIEW04-GRE-Test-2018_313-462.indd 444 12/05/17 12:07 pm