Question

2i/5c level 2
1 the line graphed on the grid represents the first of two equations in a system of linear equations.

the graph of the second equation in the system passes through the point \\((2, 2)\\) and has a slope of \\(\frac{3}{4}\\). which system of equations does the graph represent?

a
\\y = -\frac{3}{2}x + 1\\
\\y = \frac{3}{4}x + \frac{1}{2}\\

b
\\y = -\frac{3}{2}x + 1\\
\\y = 2x + \frac{3}{4}\\

c
\\y = -\frac{2}{3}x + 1\\
\\y = \frac{3}{4}x + 2\\

d
\\y = -\frac{2}{3}x + 1\\
\\y = \frac{3}{4}x + \frac{1}{2}\\

Explanation:

Find the equation of the graphed line

Using the Slope-Intercept Form knowledge point

$$
LATEXBLOCK0
$$

Find the equation of the second line

Using the Slope-Intercept Form knowledge point

$$
LATEXBLOCK1
$$

Match with the given options

Using the Systems of Linear Equations knowledge point

$$
LATEXBLOCK2
$$

This matches option D.

Answer:

• (A) \(

$$\begin{cases} y = -\frac{3}{2}x + 1 \\ y = \frac{3}{4}x + \frac{1}{2} \end{cases}$$

\)

• (B) \(

$$\begin{cases} y = \frac{3}{2}x + 1 \\ y = 2x + \frac{3}{4} \end{cases}$$

\)

• (C) \(

$$\begin{cases} y = \frac{2}{3}x + 1 \\ y = \frac{3}{4}x + 2 \end{cases}$$

\)

• **(D) \(

$$\begin{cases} y = -\frac{2}{3}x + 1 \\ y = \frac{3}{4}x + \frac{1}{2} \end{cases}$$

\) (Correct answer)**