# PSAT Math : How to graph a line

## Example Questions

### Example Question #1 : How To Graph A Line

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 #2 : How To Graph A Line

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

I

II

Cannot be determined

IV

III

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 #3 : How To Graph A Line

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 #4 : How To Graph A Line

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 #5 : How To Graph A Line

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