How is the graph mc019-1.jpg related to the graph of mc019-2.jpg? A Guide to Linear Functions

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!