how do you graph this?

Question

y=4x+3

y=-x-2

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Answer 1

Let us remember the formula y=mx+b.

y=4x+3

Here, b=3. You will start by placing a dot on the y-axis at (0,3). In the formula, m signifies the slope. Here, the slope would be 4/1 (the one in the denominator because 4 is a whole number). Remember, the numerator means you count up or down, and the denominator means you count left or right. Because the slope (m) is a positive number, you will start at (0,3) and move up on the y-axis by 4 spaces, and right by one space. This should bring you to (1,7) for your second point. Your third point will start at (0,3) again, and instead of going up by 4 spaces, we will go down by 4 spaces and to the left by 1 space (this creates -4/-1 which is the same thing as 4/1 because remember the negatives cancel out each other if they're in the numerator and denominator). This should make your third point at (-1,0) and your line looking like /.

y=-x-2

Here, we have a minus sign for the y-axis (right before the b value). Let us start by placing our first point at (0,-2). For our slope (m), we see a negative value of -1. This also means -1/1. Please note that just because we have a negative in the numerator does not mean that we also have a negative in the denominator because, again, they will cancel each other out to create a positive. Using what we learned in the first equation above, we can go ahead and start at (0,-2) and count down by 1 space and this time count right by one space (because of the negative we go in the opposite direction). This makes our second point at (1,-3). Doing the same thing but flipped (1/-1), we start at (0,-2) and count up by one space, then to the left by one space. This should make your last point at (-1,-1) and your line looking like \.

Answer 2

both are straight lines

1st is a somewhat steep upward sloping line with slope =4 and y intercept =3

2nd is a downward sloping line with slope =-1, it's going downhill at a 45 degree angle, with y intercept=-2

they intersect at the point (-1,-1) in the 3rd quadrant

x intercept for the 1st line is -3/4 = -0.75

x intercept for the 2nd line is =-2

plot the 2 points for the 1st line, (0,3) and (-3/4,0) and connect them with a straight line

plot the 2 points for the 2nd line (0,-2) and (-2,0) and connect them with a straight line

those two points for each line are the y and x intercepts