Question

question 12
1 pts
ma.912.f.1.5
which function has the greatest slope?
a. $y = \frac{7}{4}x + 2$
b. $y = -\frac{3}{2}x + 6$
c. $y = \frac{4}{3}x - 7$
d. $y = \frac{9}{5}x + 1$
a
b
c
d

Explanation:

Step1: Recall slope-intercept form

The slope - intercept form of a linear function is \(y = mx + b\), where \(m\) is the slope. So we need to find the slope (\(m\)) of each function:

• For option A: \(y=\frac{7}{4}x + 2\), the slope \(m_A=\frac{7}{4}=1.75\)
• For option B: \(y =-\frac{3}{2}x+6\), the slope \(m_B =-\frac{3}{2}=- 1.5\)
• For option C: \(y=\frac{4}{3}x - 7\), the slope \(m_C=\frac{4}{3}\approx1.33\)
• For option D: \(y=\frac{9}{5}x + 1\), the slope \(m_D=\frac{9}{5}=1.8\)

Step2: Compare the slopes

We compare the values of \(m_A = 1.75\), \(m_B=-1.5\), \(m_C\approx1.33\), and \(m_D = 1.8\). Since \(1.8>1.75>1.33>- 1.5\), the slope of the function in option D is the greatest.

Answer:

D. \(y=\frac{9}{5}x + 1\)