I am going to change the problem by looking at the functions
y = 3x + 9 and y = -5x - 3
The first thing I would do is to use a piece of scrap paper and draw a rough sketch using the intercepts. For the first function
y = 3x + 9
When x = 0, y = 9 so (0,9) is on the graph and when y = 0, x = -3 so (-3,0) is on the graph.
Now add the second function
y = -5x - 3
When x = 0, y = -3 so (0,-3) is on the curve. When y = 0, x = -3/5
I purposefully didn't mark the x-intercept of the second line on the graph and drew the line thick because I am not trying to be accurate here, I am just trying to see what ranges I should choose for the x and y values when I draw an accurate graph. What I see here is that if I draw a graph with the x values between -4 and 1, and the y values between -1 and 10 then the point where the lines cross will be on my graph.
To graph the second line I substituted x = -1 and got y = 2 to find a second point on the graph. I used this point rather than the x-intercept so that I didn't have to use fractions. I also didn't mark a scale on the axes, but you will need to do this to answer part 3.
The equations are
y = 3x + 9
y = -5x - 3
hence
3x + 9 = -5x - 3
Simplifying gives me
8x = 12 or x = -2/3
Substituting this value into the first equation I get y = 9/2
This looks approximately correct on my diagram, that is the curves intersect at x = -2/3, y = 9/2
Penny
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