# PSAT Math : Graphing

## Example Questions

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### Example Question #18 : Graphing Lines

A line graphed on the coordinate plane below.

Give the equation of the line in slope intercept form.

Explanation:

The slope of the line is  and the y-intercept is .

The equation of the line is

### Example Question #1 : Graphing

Give the equation of the curve.

Explanation:

This is the parent graph of . Since the graph in question is negative, then we flip the quadrants in which it will approach infinity. So the graph of  will start in quadrant 2 and end in 4.

### Example Question #51 : New Sat Math Calculator

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

II

IV

III

Cannot be determined

I

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 : Graphing

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

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 #3 : Graphing

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

Explanation:

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 #4 : Graphing

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

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

### Example Question #4 : How To Graph An Ordered Pair

Which of the following coordinate pairs is farthest from the origin?

Explanation:

Using the distance formula, calculate the distance from each of these points to the origin, (0, 0). While each answer choice has coordinates that add up to seven, (-1, 8) is the coordinate pair that produces the largest distance, namely , or approximately 8.06.

### Example Question #1 : Graphing

A point at  in the standard coordinate plane is shifted right 5 units and down 3 units.  What are the new coordinates of the point?

Explanation:

The point  shifted to the right 5 units will shift along the x-axis, meaning that you will add 5 to the original x-coordinate, so the new . The point shifted down by three units will shift down the y-axis, meaning that you will subtract three from the original y-coordinate, so the new .

The resultant coordinate is .

### Example Question #6 : Graphing

Give the coordinates of the point plotted in the above set of coordinate axes.

None of the other responses is correct.

Explanation:

The point can be reached from the origin by moving 2 units right then 6 units up. This makes the first coordinate 2 and the second coordinate 6.

### Example Question #6 : How To Graph A Function

Which of the following could be a value of  for ?