PSAT Math : How to graph a line

Study concepts, example questions & explanations for PSAT Math

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Example Questions

Example Question #665 : Geometry

A line graphed on the coordinate plane below. Graph_of_y_-2x_4

Give the equation of the line in slope intercept form. 

Possible Answers:

\dpi{100} \small y=2x-4

\dpi{100} \small y=-2x+4

\dpi{100} \small y=2x+4

\dpi{100} \small y=-2x-4

\dpi{100} \small y=-x+4

Correct answer:

\dpi{100} \small y=-2x+4

Explanation:

The slope of the line is \dpi{100} \small -2 and the y-intercept is \dpi{100} \small 4.

The equation of the line is \dpi{100} \small y=-2x+4

Example Question #1 : How To Graph A Line

Graph_of_y_-x_3

Give the equation of the curve. 

Possible Answers:

None of the other answers

\dpi{100} \small y=-x^{2}

\dpi{100} \small y=x^{3}

\dpi{100} \small y=x^{4}

\dpi{100} \small y=-x^{3}

Correct answer:

\dpi{100} \small y=-x^{3}

Explanation:

Graph_of_x_3This is the parent graph of \dpi{100} \small x^{3}. Since the graph in question is negative, then we flip the quadrants in which it will approach infinity. So the graph of \dpi{100} \small y=-x^{3} will start in quadrant 2 and end in 4. 

Example Question #23 : Graphing

The equation  represents a line.  This line does NOT pass through which of the four quadrants?

Possible Answers:

I

II

Cannot be determined

IV

III

Correct answer:

III

Explanation:

Plug in  for  to find a point on the line:

Thus,  is a point on the line.

Plug in   for  to find a second point on the line:

 is another point on the line.

Now we know that the line passes through the points  and .  

A quick sketch of the two points reveals that the line passes through all but the third quadrant.

Example Question #2 : How To Graph A Line


Psat1question

What is the equation of the line in the graph above?

Possible Answers:

Correct answer:

Explanation:

In order to find the equation of a line in slope-intercept form , where  is the slope and  is the y-intercept), one must know or otherwise figure out the slope of the line (its rate of change) and the point at which it intersects the y-axis. By looking at the graph, you can see that the line crosses the y-axis at .  Therefore, .

Slope is the rate of change of a line, which can be calculated by figuring out the change in y divided by the change in x, using the formula 

.  

When looking at a graph, you can pick two points on a graph and substitute their x-  and y-values into that equation.  On this graph, it's easier to choose points like and .  Plug them into the equation, and you get 

Plugging in those values for  and  in the equation, and you get 

Example Question #122 : Psat Mathematics

What are the x- and y- intercepts of the equation ?

Possible Answers:

Correct answer:

Explanation:

Answer: (1/2,0) and (0,-2)

Finding the y-intercept: The y-intercept is the point at which the line crosses tye y-axis, meaning that x = 0 and the format of the ordered pair is (0,y) with y being the y-intercept.  The equation  is in slope-intercept () form, meaning that the y-intercept, b, is actually given in the equation.  b = -2, which means that our y-intercept is -2.  The ordered pair for expressing this is (0,-2)

Finding the x-intercept: To find the x-intercept of the equation , we must find the point where the line of the equation crosses the x-axis.  In other words, we must find the point on the line where y is equal to 0, as it is when crossing the x-axis.  Therefore, substitute 0 into the equation and solve for x: 

The x-interecept is therefore (1/2,0).  

Example Question #123 : Psat Mathematics

Which of the following could be the equation of the line shown in this graph?

Line

Possible Answers:

Correct answer:

Explanation:

The line in the diagram has a negative slope and a positive y-intercept. It has a negative slope because the line moves from the upper left to the lower right, and it has a positive y-intercept because the line intercepts the y-axis above zero. 

The only answer choice with a negative slope and a positive y-intercept is 

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