equation 1: 4x-2y=16

Question

equation 2: y=-4/5x+2
equation 3: y-4=3(x+5)

which statement is true?

A. line 1 has the greatest slope
B. line 2 has the biggest y intercept
C. line 2 has an increasing graph
D. line 1 has the biggest y intercept
E. line 3 has a decreasing graph
F. line 3 has the greatest slope

Answer 1

To determine the statement that is true, let's analyze each of the equations:

Equation 1: 4x - 2y = 16
To find the slope of this equation, we need to rearrange it in slope-intercept form (y = mx + b), where m represents the slope:
-2y = -4x + 16
y = 2x - 8

The slope of this equation is 2, which means that it is not the greatest slope.

Equation 2: y = -4/5x + 2
In this equation, the slope is -4/5, which is smaller than 2. Therefore, it is also not the greatest slope.

Equation 3: y - 4 = 3(x + 5)
To determine the slope, we need to rewrite the equation in slope-intercept form:
y - 4 = 3x + 15
y = 3x + 19

The slope of this equation is 3, which is the greatest slope among all three equations.

In conclusion, the statement that is true is F. line 3 has the greatest slope.