Answer:
1 - green line: y = 5x + 2
2 - red line: y = 3x + 3
3 - blue line: y = 2x + 3
Step-by-step explanation:
1 - green line
The graph with the green line is the easiest to match with an equation.
If you look at the graph, you see that when x = 0, the y-value is 2.
There's only one of the given equations that y = 2 when x = 0, the first one.
y = 5x + 2
y = 5 (0) + 2 = 0 + 2 = 2
It's easy to spot, because in the format y = mx + b, the b is the value of Y when x = 0, as we just demonstrated.
2 - Red line
In this case, when x = 0, y = 3. And there are 2 equations for which it's true... which is normal because the blue line (in next graph) also passes by this point.
Then to know which equation goes with the red line graph, we have two choices...
A. determine the slope (rate of change) of the red line and see if it matches one of the equations.
B. See what value of X yields a value of 0 for Y and see where it would land on the X-axis.
The second method is faster. If you see on the graph, when y = 0, x = -1
If we take the 2nd equation (y = 3x + 3) and we set the value of y to 0, we have:
0 = 3x + 3
-3 = 3x
x = -1
Which is exactly what we wanted to find.
So, the red line is y = 3x + 3
3. blue line
Well, there's only one answer left (y = 2x + 3), so it's easy... but let's make sure by finding the slope (method A listed for the red line above), in case your teacher would be playing tricks on you.
The slope of a line is the variation of y-value (Δy) divided by the variation of x-value (Δx).
If we take the two points where the blue line crosses the axis, we have (-1.5, 0) and (0,3).
Now, let's calculate the slope:
S = (0 - 3) / (-1.5 - 0) = -3 / -1.5 = 2
And 2 is the slope of the equation y = 2x + 3
So, we're good.
