Contents
Introduction
In this article, we will explore how two graphs of linear functions are related to each other. We will use the graphs mc019-1.jpg and mc019-2.jpg as examples. These graphs are shown below:
A linear function is a function that can be written in the form y = mx + b, where m is the slope and b is the y-intercept. The graph of a linear function is a straight line.
How to compare two graphs of linear functions
To compare two graphs of linear functions, we can look at their slopes and y-intercepts. The slope tells us how steep the line is and the direction it goes. The y-intercept tells us where the line crosses the y-axis.
To find the slope of a line, we can use the formula m = (y2 – y1) / (x2 – x1), where (x1, y1) and (x2, y2) are any two points on the line. To find the y-intercept of a line, we can plug in x = 0 into the equation of the line and solve for y.
Comparing mc019-1.jpg and mc019-2.jpg
Let’s apply these steps to compare the graphs mc019-1.jpg and mc019-2.jpg.
Slope
To find the slope of mc019-1.jpg, we can use any two points on the line. For example, we can use (0, 4) and (4, 0). Plugging these into the slope formula, we get:
m = (0 – 4) / (4 – 0)
m = -4 / 4
m = -1
So, the slope of mc019-1.jpg is -1.
To find the slope of mc019-2.jpg, we can use any two points on the line. For example, we can use (0, 6) and (3, 0). Plugging these into the slope formula, we get:
m = (0 – 6) / (3 – 0)
m = -6 / 3
m = -2
So, the slope of mc019-2.jpg is -2.
We can see that both lines have negative slopes, which means they go down from left to right. However, mc019-2.jpg has a steeper slope than mc019-1.jpg, which means it goes down faster.
Y-intercept
To find the y-intercept of mc019-1.jpg, we can plug in x = 0 into its equation and solve for y. Since we know its slope is -1, we can write its equation as y = -x + b. Plugging in x = 0, we get:
y = -(0) + b
y = b
So, the y-intercept of mc019-1.jpg is b. Looking at the graph, we can see that b = 4, so the y-intercept is 4.
To find the y-intercept of mc019-2.jpg, we can plug in x = 0 into its equation and solve for y. Since we know its slope is -2, we can write its equation as y = -2x + b. Plugging in x = 0, we get:
y = -(0) + b
y = b
So, the y-intercept of mc019-2.jpg is b. Looking at the graph, we can see that b = 6, so the y-intercept is 6.
We can see that both lines have positive y-intercepts, which means they cross the y-axis above the origin. However, mc019-2.jpg has a higher y-intercept than mc019-1.jpg, which means it starts higher on the y-axis.
Conclusion
We have compared two graphs of linear functions by looking at their slopes and y-intercepts. We have found that:
- Both lines have negative slopes, but mc019-2.jpg has a steeper slope than mc019-1.jpg.
- Both lines have positive y-intercepts, but mc019-2.jpg has a higher y-intercept than mc019-1.jpg.
Therefore, we can say that the graph of mc019-2.jpg is related to the graph of mc019-1.jpg by being steeper and higher on the y-axis.
According to Wyzant, the equation of mc019-1.jpg is y = -x + 4. According to Brainly, the equation of mc019-2.jpg is y = -2x + 6. We can verify these equations by plugging in some points from the graphs and checking if they satisfy them. For example, (0, 4) and (4, 0) are on mc019-1.jpg, and (0, 6) and (3, 0) are on mc019-2.jpg. Plugging these into the equations, we get:
y = -x + 4
4 = -(0) + 4 (true)
0 = -(4) + 4 (true)
y = -2x + 6
6 = -(0) + 6 (true)
0 = -(3) + 6 (true)
So, the equations are correct.
I hope this article has helped you understand how to compare two graphs of linear functions. Thank you for reading!
