You will need to enter those equations into a graphing calculator, if allowed, or do it the old-fashioned way on graphing paper.
To do it on graphing paper, you technically only need two points that lie on each line to connect them and graph your line. However, I like to find three points of each line in case to avoid the chance that I made a mistake somewhere.
You also can solve this by finding the y-intercept and the slope and plotting, but let's do it by finding a set of three points that lie on each line.
FIRST LINE: y = –4x + 3
Let's say we want to find the y-values when x is 0, when x is 2, and when x is –2.
So, we are going to have three points: (0,y1), (2,y2), and (–2,y3)
To get the first point, substitute 0 for x in the equation to get:
y = –4(0) + 3
y = 0 + 3
y = 3
Now we know the point (0,3) is on the FIRST LINE.
To get the second point, substitute 2 for x in the equation to get:
y = –4(2) + 3
y = –8 + 3
y = –5
Now we know the point (2,–5) is on the FIRST LINE.
To get the third point, substitute –2 for x in the equation to get:
y = –4(–2) + 3
y = 8 + 3
y = 11
Now we know the point (–2,11) is on the FIRST LINE.
Plot those three points. Connect them, using a ruler, to make a straight line segment; put arrows on the each end to show that the line goes on forever in each direction.
Repeat what I just did for your SECOND LINE, 4x – 2y = 6. Use whatever values for the coordinates of x that you like. I always like to use 0, because the math is easiest that way. Maybe use 1 and –1 for the other x-coodinates.
You may want to put the equation for the SECOND LINE in the point-slope form that the other one was already in. I will do this for you and let you do the rest.
4x – 2y = 6
–4x –4x
–2y = –4x + 6
____ ________
–2 –2
y = 2x – 3 (work with this equation to find three points on the line)
