How To Graph Negative Slope

Graphing Equations in Slope Intercept Class

Learning Objective(s)

· Give the slope intercept grade of a linear equation and define its parts.

· Graph a line using the gradient intercept formula and derive the equation of a line from its graph.

Introduction

Straight lines are produced by linear functions. That means that a straight line can be described by an equation that takes the form of the linear equation formula, . In the formula, y is a dependent variable, x is an independent variable, m is a constant rate of alter, and b is an adjustment that moves the function away from the origin. In a more full general straight line equation, ten and y are coordinates, grand is the gradient, and b is the [y-intercept]. Because this equation describes a line in terms of its gradient and its y-intercept, this equation is chosen the slope-intercept form.

Gradient Intercept Formula

The graph below represents whatsoever line that tin can be written in slope intercept form. It has two slider bars that can be manipulated. The bar labeled k lets you adjust the slope, or steepness, of the line. The bar labeled b changes the y-intercept. Effort sliding each bar dorsum and forth, and see how that affects the line.

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That was fun, eh? You should have noticed that changing the value of one thousand could swivel the line from horizontal to about vertical and through every gradient in between. As m, the slope, gets larger, the line gets steeper. When yard gets smaller, the slope flattens.

Irresolute the value of b moved the line around the coordinate plane. A positive y-intercept means the line crosses the y-axis above the origin, while a negative y-intercept means that the line crosses beneath the origin.

But by changing the values of 1000 and b, we can define any straight line. That's how powerful and versatile the slope intercept formula is.

How is the x-intercept represented in the slope intercept form of a linear equation?

A) It is represented by 10.

B) It is represented by m.

C) It is represented past b.

D) It is non represented.

Show/Hibernate Answer

A) It is represented by x.

Incorrect. 10 is an x-coordinate, but not the x-intercept. The gradient intercept class of a linear equation is based on the slope and the y-coordinate at the y-intercept. The correct reply is that it is not represented.

B) It is represented past m.

Incorrect. one thousand is the slope of the line. The slope intercept grade of a linear equation is based on the gradient and the y-coordinate at the y-intercept. The correct answer is that information technology is non represented.

C) It is represented by b.

Incorrect. b is the y-coordinate at the y-intercept. The gradient intercept course of a linear equation is based on the slope and the y-coordinate at the y-intercept. The right reply is that it is not represented.

D) It is not represented.

Correct. The slope intercept form of a linear equation is based on the slope and the y-coordinate at the y-intercept.

From Graph to Equation

Now that we understand the gradient intercept form, we tin look at the graph of a line and write its equation just from identifying the slope and the y-intercept. Permit'south try it with this line:

The gradient intercept form is . For this line, the slope is , and the y-intercept is 4. If we put those values into the formula, we go the equation . That's the slope intercept equation of our line.

What is the equation of the line in the graph beneath?

Testify/Hide Reply

Incorrect. You accept inverted the slope. The correct gradient of this line is and the y-intercept is -three. The correct answer is .

Right. The slope of this line is and the y-intercept is -3.

Wrong. iv is the 10-intercept, non the slope. The gradient of this line is and the y-intercept is -three. The correct answer is.

Wrong. The gradient is positive and the y-intercept is negative, non the other way effectually. The correct answer is .

From Equation to Graph

We've seen that information technology'due south not difficult to convert the graph of a line to an equation. We can also piece of work the other manner and produce a graph from a slope intercept equation. Consider the equation . This equation tells us that the y-intercept is at -1. We'll start by plotting that point, (0, -one), on a graph.

The equation as well tells u.s. that the gradient of this line is -iii. So we'll count upwards 3 units and over -1 unit of measurement and plot a second indicate. (We could also accept gone down 3 and over +one.) And so we draw a line through both points, and there it is, the graph of .

Which graph shows the line ?

A) B)

C) D)

Show/Hibernate Answer

A) Graph A

Correct. This line has a positive y-intercept and a steep positive slope, every bit the equation requires.

B) Graph B

Incorrect. This line has a gentle gradient, while the equation specifies a steep slope. The correct respond is Graph A.

C) Graph C

Incorrect. This line has a negative y-intercept and a negative slope, while the equation specifies a positive y-intercept and a steep positive gradient. The correct respond is Graph A.

D) Graph D

Incorrect. This line has a negative y-intercept and a gentle slope, while the equation specifies a positive y-intercept and a steep positive slope. The correct respond is Graph A.

Summary

The gradient intercept form of a linear equation is written as , where m is the slope and b is the value of y at the y-intercept. Because we only demand to know the slope and the y-intercept to write this formula, it is fairly easy to derive the equation of a line from a graph and to depict the graph of a line from an equation.