McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
6. Inequalities in Two Triangles
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Exercise 45 Page 462

Focus on the sign of the slope and the y-intercept.

F

Practice makes perfect
The equations in all options are given in slope-intercept form. y= mx+ b In this form m is the slope and (0, b)) is the y-intercept of the line. A positive slope indicates an increasing function, a negative slope indicates a decreasing function.

Let's find the sign of m and b for the graph shown.

  • The graph is decreasing, so m<0.
  • The graph intersects the y-axis above the x-axis, so b>0.

Let's look at the options and find the equation with a negative slope and a positive y-intercept.

Option Equation Is m negative? Is b positive?
F y= - 1/4x +5 Yes, - 1/4<0 Yes, 5>0
G y= - 1/4x -5 Yes, - 1/4<0 No, - 5<0
H y= 1/4x +5 No, 1/4>0 Yes, 5>0
J y= 1/4x -5 No, 1/4>0 No, - 5<0

The correct answer is F.