Question

What is the slope of a line that is parallel to the line shown on the graph?
A.–3
B.-1/3
C.1/3
D. 3

Answer 1

If we count from the point (0, 2), where the line goes through the y-axis, to the point where it goes through (1, -1) we are moving down 3 units (from 2 to -1 is 3 units) and over to the right 1 unit.  So the slope of this line is -3.  Negative slopes always go from upper left to lower right, whereas positive slopes always go from lower left to upper right.  So we know this is a negative slope.  Parallel lines by definition have the exact same slope, so a line parallel to this one will also have a slope of -3.

Answer 2

The slope of a line that is parallel to the line shown on the graph is -3.

What is slope of a line?

The slope or gradient of a line is a number that describes both the direction X and Y and the steepness of the line. It is the ratio of the vertical change to the horizontal change between any two distinct points on a line.

For the given situation,

The slope of a line from its graph by looking at the rise and run.

The vertical change between two points is called the rise, and the horizontal change is called the run.

One characteristic of a line is that its slope is constant all the way along it. So, you can choose any 2 points along the graph of the line to figure out the slope.

Now take points (0,2) and (1,-1)

$Slope = \frac{rise}{run}$

Line slants down from left to right. So line has a negative slope.

⇒ $Slope =\frac{y2-y1}{x2-x1}$

⇒ $Slope =\frac{-1-2}{1-0}$

⇒ $Slope = -3$  

The slope of the line that is parallel to the given line is same as that of the line.

Hence we can conclude that the slope of a line that is parallel to the line shown on the graph is -3.

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