Question

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1. which graph best represents the line ( x - y = 3 )?

a. graph b. graph c. graph d. graph
cadba

1. identify the equation of the line graphed below.

graph
a. ( x + 2y = -2 )
b. ( x - 2y = 2 )
c. ( 2x + y = -1 )
d. ( 2x - y = 1 )

1. what is the slope of the line ( x = -5 )?

a. -5
b. 5
c. 0
d. undefined

1. which equation represents a line parallel to

the ( y )-axis?
a. ( y = x )
b. ( x = 4 )
c. ( y = 4 )
d. ( y = x + 4 )

1. which is the equation of the line that passes through

the points (-4, 8) and (1, 3)?
a. ( y = -x + 4 )
b. ( y = -x + 12 )
c. ( y = x + 4 )
d. ( y = x + 12 )

Explanation:

Question 1:

Step1: Rewrite the equation

Rewrite \(x - y = 3\) in slope - intercept form \(y=mx + b\) (where \(m\) is the slope and \(b\) is the y - intercept). We get \(y=x - 3\). The slope \(m = 1\) (positive slope) and the y - intercept \(b=-3\) (the line crosses the y - axis at \((0,-3)\)).

Step2: Analyze the graphs

• Graph A: Has a positive slope and a positive y - intercept.
• Graph B: Has a negative slope.
• Graph C: Has a positive slope and a negative y - intercept (matches \(y = x-3\)).
• Graph D: Has a negative slope.

Step1: Find two points on the line

From the graph, we can identify two points. Let's assume we find two points \((x_1,y_1)\) and \((x_2,y_2)\). Let's say we pick two points, for example, when \(x = 0\), we can find \(y\), and when \(y = 0\), we can find \(x\).
Let's test each option:

• Option A: \(x + 2y=-2\). When \(x = 0\), \(2y=-2\), \(y=-1\). When \(y = 0\), \(x=-2\).
• Option B: \(x - 2y = 2\). When \(x = 0\), \(-2y=2\), \(y=-1\)? No, \(-2y = 2\Rightarrow y=-1\)? Wait, \(x-2y = 2\), when \(x = 0\), \(y=-1\); when \(y = 0\), \(x = 2\).
• Option C: \(2x + y=-1\). When \(x = 0\), \(y=-1\); when \(y = 0\), \(x=-\frac{1}{2}\).
• Option D: \(2x - y = 1\). When \(x = 0\), \(-y = 1\), \(y=-1\)? No, \(-y=1\Rightarrow y = - 1\); when \(y = 0\), \(2x=1\), \(x=\frac{1}{2}\).

Looking at the graph, let's find two points. Suppose the line passes through \((0, - 1)\) and \((-1,1)\)? Wait, let's use the slope - intercept form. Let's take two points from the graph. Let's assume the line passes through \((0,-1)\) and \((2, - 2)\). The slope \(m=\frac{-2 + 1}{2-0}=-\frac{1}{2}\).

For option A: \(x + 2y=-2\Rightarrow2y=-x - 2\Rightarrow y=-\frac{1}{2}x-1\). The slope is \(-\frac{1}{2}\) and y - intercept is \(-1\), which matches.

Step1: Recall the slope formula for vertical lines

The line \(x=-5\) is a vertical line. The slope of a vertical line is undefined because the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\), and for a vertical line, \(x_2=x_1\), so the denominator is zero.

Answer:

C

Question 2: