Question

graph the given system of linear equations.
x = -3
y = \frac{1}{4}x + 2
**choose the correct line to graph: line 1 is line ab, line 2 is line cd
click to select
line ab
line cd

Explanation:

Step1: Analyze \( x = -3 \)

The equation \( x = -3 \) is a vertical line. It passes through all points where the x - coordinate is - 3. So, for example, the points \((-3,0)\), \((-3,1)\), \((-3, - 1)\) lie on this line.

Step2: Analyze \( y=\frac{1}{4}x + 2 \)

This is a linear equation in slope - intercept form \( y=mx + b \), where the slope \( m=\frac{1}{4} \) and the y - intercept \( b = 2 \). The y - intercept means the line crosses the y - axis at \((0,2)\). To find another point, we can use the slope. The slope \( \frac{1}{4} \) means for every 4 units we move to the right (increase in x by 4), we move up 1 unit (increase in y by 1). So if we start from \((0,2)\) and move 4 units to the right (x = 4) and 1 unit up (y=3), we get the point \((4,3)\).

To graph the system:

• For \( x=-3 \), draw a vertical line passing through \( x = - 3 \) on the coordinate plane.
• For \( y=\frac{1}{4}x + 2 \), plot the y - intercept \((0,2)\) and the point \((4,3)\) (or other points found using the slope) and draw a line through them.

If we assume Line AB is for \( x = - 3 \) (vertical line) and Line CD is for \( y=\frac{1}{4}x+2 \) (slanted line with positive slope), then we select Line AB for \( x=-3 \) and Line CD for \( y = \frac{1}{4}x+2 \) (or vice - versa depending on the actual line definitions, but based on the nature of the lines: vertical line is \( x=-3 \), non - vertical with slope \( \frac{1}{4} \) is \( y=\frac{1}{4}x + 2 \)).

Answer:

To graph \( x=-3 \), use the vertical line (e.g., Line AB) passing through \( x=-3 \). To graph \( y = \frac{1}{4}x+2 \), use the line (e.g., Line CD) with y - intercept at \((0,2)\) and slope \( \frac{1}{4} \). If choosing the correct line for \( x=-3 \) (vertical) as Line AB and for \( y=\frac{1}{4}x + 2 \) (slanted) as Line CD, then:

• For \( x=-3 \): Select Line AB.
• For \( y=\frac{1}{4}x + 2 \): Select Line CD.