Graph the function g (x) = 3/5x - 2

Answer 1

Graph g(x)=(3/5)x-2

The slope is 3/5 where 3 is the rise and 5 is the run. The number -2 is the y-intercept.

Starting at the y-intercept, (0,-2), put a dot there. From the y-intercept move 5 units to the right and then move 3 units up. Put a dot there at (5,1). Repeat the procedure, Move 5 units right and 3 units up. Put a point there at (10,4). You now have three collinear points and you can connect the dots and you have your graph.

However, if you would like to plot some points below the y-intercept to make the graph look better, you can make the slope be (-3)/(-5) because a negative divided by a negative is positive. Starting at the y-intercept move 5 units left and 3 units down to get to (-5,-5). Put a dot there and repeat the procedure and you are now at (-10,-8). Put a dot there and connect all the dots and you have your graph with points both above and below the y-intercept.

Answer 2

Hi Jamal J

First of all, please let us know what exactly you have above

Is it the line

g(x) = (3/5)x - 2

OR

g(x) = 3/(5x - 2)

In both above g(x) is the y coordinate or values you generate when you enter values for x.

In either case you can set x = 0 to get the y intercept (0, g(0)) then you can set g(x) or y to zero and solve for x to get the x intercept (x, 0).

For example

If your function is

g(x) = (3/5)x - 2

The above is a line in Slope Intercept Form; y = mx + b, where m is (3/5) and b is -2

When x = 0

g(0) = (3/5)0 - 2

g(0) = 0 - 2

g(0) = -2

So you have the y intercept (0, -2)

If you set y or g(x) = 0 then

0 = (3/5)x - 2

You can simply solve for x

Add 2 to both sides to give

2 = (3/5)x

Multiply both sides by (5/3) to give

10/3 = x

This is your second point (10/3, 0)

Now you have two points, your x and y intercepts, to draw a line through on a grid (10/3, 0) and (0, -2)

If g(x) = 3/(5x -2) then the denominator, (5x -2) cannot be zero so x cannot be (2/5) because

5(2/5) = 2 this would result in division by zero, because

g(2/5) = 3/(2-2) or 3/0 and we don’t want division by zero.

The value (2/5) would be a barrier or asymptote on your graph.

Are you graphing by hand, using a graphing calculator or desmos.com?

You can graph your function by hand by setting up a table of x and g(x) values then graphing them on an x, y grid by just plotting the points from your table. You can use a graphing calculator or you can see if your graph is correct by checking it out at desmos.com

I hope this helps.