# PSAT Math : How to graph a line

## Example Questions

### Example Question #661 : Geometry

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 #2 : 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 #53 : New Sat Math Calculator

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

III

IV

Cannot be determined

II

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 #1 : 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 #1 : 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 ### All PSAT Math Resources 