Hi Jinny L
I am going to assume that your lines are to be plotted by hand or by you selecting x values in order to calculate y values then plot the (x,y) coordinates on some interactive grid. Please let me know if this is correct.
Item 1 is in the form of y = mx + b also called Slope Intercept Form and you can just make a list of x values, then perform the calculation to get the y value and plot the (x,y) coordinates on a grid. You can look up Slope Intercept Form in your text or online.
Except for items 2 and 5 you can solve all items as y in terms of x in the Slope Intercept format above.
Two of the easiest points to plot are the x and y intercepts
To find the y intercept set x equal to zero and solve for y
To find the x intercept set y equal to zero and solve for x
Since item 3 looks the most complicated (but it’s really not) I will put it in Slope Intercept Form for you.
3.) 3x + 4y -12 = 0
Solve the equation for y by subtracting 3x and adding 12 to each side, this gives
4y = -3x + 12
Next divide each term by 4
y = -(3/4)x + 3
If you set x equal to zero then y = 3 and you have the point (0, 3)
If you set y equal to zero then x = 4 and you have the point (4,0)
If you set x equal to 8 then y = -3 and you have the point (8, -3)
Item 2 is a horizontal line parallel to the x axis, it has no x intercept
Item 2 can only be solved for y
2.) y - 3 = 0
y = 3
In this type of line y has the same value, 3, for any value of x
Item 5 is a vertical line parallel to the y axis, it has no y intercept
Item 5 can only be solved for x
5.) x + 5/2 = 0
x = -5/2
In this line x has the same value, -5/2, for any value of y
You should draw all your lines to see what they illustrate.
Your 5 items above show all the types of single Lines and Slopes, m, you have a positive slope in item 1, a negative slope in item 3, a zero slope in item 2, an undefined slope in item 5 and in item 4 a line that passes through the origin where the x intercept and y intercept are the same.
I hope this information helps you to set y in terms of x, make your list of points and plot your lines by hand or on a given grid.
