If I were to graph 20a+34b is greater than or equal to 240, which would be the easier way: graphing it by finding the x and y intercepts, or graphing it by finding the slope and y-intercept?
since you are talking about x and y intercepts you should look at your relation as
20x + 34y ≥ 240 rather than using a and b
I usually use the x and y intercepts, since in most cases you can do them in your head.
e.g. if y = 0, x = 12
if x = 0, y = appr. 7 (actually 7.06)
so you quickly have two points that determine your line.
If the equation is in the form
y = mx + b, I mark the y-intercept, then step off to the next point by using the slope.
e.g. y = (3/4)x + 1
mark (0,2), from that point move to the right 4, then up 3 and you got your two points for the line. Real easy.
thanks
To determine which method would be easier for graphing the inequality 20a + 34b ≥ 240, let's consider both approaches:
1. Graphing by finding x and y intercepts:
The x-intercept occurs when y = 0. By substituting y = 0 into the inequality, we can solve for the x-intercept:
20a + 34(0) ≥ 240
20a ≥ 240
a ≥ 12
Similarly, the y-intercept occurs when x = 0. By substituting x = 0 into the inequality, we can solve for the y-intercept:
20(0) + 34b ≥ 240
34b ≥ 240
b ≥ 7.06 (approximately)
To graph using this method, draw a line passing through the points (12, 0) and (0, 7.06) on a Cartesian coordinate system. Since the inequality is greater than or equal to, the area above or on the line should be shaded.
2. Graphing by finding the slope and y-intercept:
To graph using this method, rewrite the inequality in slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.
Rearranging the original inequality, we have:
34b ≥ -20a + 240
b ≥ (-20/34)a + (240/34)
b ≥ (-10/17)a + (120/17)
Now, we have the equation in slope-intercept form. The slope is -10/17, and the y-intercept is 120/17. To graph, plot the y-intercept and use the slope to find another point on the line. Then, draw the line passing through these two points. Again, shade the area above or on the line since the inequality is greater than or equal to.
Comparing the two methods, graphing by finding the slope and y-intercept may be slightly easier because it involves fewer calculations. However, both methods will yield the same graph in the end. It is recommended to use the method with which you feel more comfortable.