Graph the line represented by the equation y = − 4 5 x + 2 y=-\frac45x+2

this problem we are asked to graph the line represented by the equation y equals negative four fifths x plus two, and here we have this graph that we can work with. So how do I go about solving this problem? Well, what I can recognize is slope intercept form, y equals m x plus b. This tells me my slope and my y intercept. Now I can clearly see that my slope is going to correspond to this negative four fifths right here. Now negative four fifths is the slope, which I'm also gonna write like this, negative four over five. And the reason I'm writing it like this, where I just move this negative sign to the four, is because I know that the slope is the rise over the run. And that's going to help us when it comes to graphing things. So we have now found our slope. So now that we have our slope, the next thing I need is my y intercept. My y intercept, I can see, happens at two. So because we're adding on this two, that means b equals two. Now what can I do with this information? Well, what I can see is that the y intercept happens at two, so that means if I go on to y here, the line is going to cross at two. But now I need to figure out what this line is going to look like, what its slant is gonna be. I obviously can't just draw a random line through here because we don't know which direction or how this line is going to be slanted. So that's what the slope here is going to tell me. The rise is negative four. The run is five. So what that means is going over to this point, I can rise negative four, which means since it's negative, I'm going to be going down. So we're gonna go down one, two, three, four. So that's where my rise is gonna be, and then my run is five. So we're gonna go one, two, three, four, five. And so there's our point right there. So notice here we now have two points, which means we can connect these with a line. So if I draw a line through these two points like so, this is gonna give me the equation of my line and or this is gonna give me the line on my graph. And you wanna make sure to line these up very carefully just so it goes through both points. That looks pretty accurate right there. So this is gonna be my line, and that would be the solution to this problem. So this is how you can graph the line given the equation in slope intercept form. Hope you found this helpful, and let's move on.

Indice

Skip topic navigation

1. Review of Real Numbers2h 39m

Simplifying Fractions
30m

Evaluating Exponents
29m

Evaluating Expressions
15m

Translating Phrases to Expressions
16m

Translating Sentences to Equations
9m

The Distributive Property
17m

Simplifying Expressions
40m

2. Linear Equations and Inequalities3h 38m

The Addition and Subtraction Properties of Equality
41m

The Multiplication and Division Properties of Equality
30m

Solving Linear Equations
1h 14m

Linear Inequalities in One Variable
1h 11m

3. Solving Word Problems2h 43m

Introduction to Problem Solving
37m

Formulas
21m

Percent Problem Solving
59m

Mixture Problem Solving
43m

4. Graphing Linear Equations in Two Variables3h 17m

The Rectangular Coordinate System
44m

Graph Linear Equations in Two Variables
24m

Graph Linear Equations Using Intercepts
23m

Slope of a Line
44m

Slope-Intercept Form
38m

Point Slope Form
22m

5. Systems of Linear Equations1h 43m

Solving Systems of Linear Equations by Graphing
41m

Solving Systems of Linear Equations by Substitution
15m

Solving Systems of Linear Equations by Elimination
45m

6. Exponents and Polynomials3h 25m

The Product Rule
10m

The Quotient Rule
13m

Intro to the Power Rules
18m

The Power of a Quotient Rule
18m

Negative Exponents
28m

Simplifying Exponential Expressions Using All Exponent Rules
6m

Intro to Polynomials
21m

Adding and Subtracting Polynomials
20m

Multiplying Polynomials
33m

Special Products
34m

7. Factoring2h 42m

Factoring by Greatest Common Factor & Grouping
38m

Factoring Trinomials of the Form x² + bx + c
11m

Factoring Trinomials of the Form ax² + bx + c
37m

Factoring Special Products
33m

Quadratic Equations & Applications
41m

8. Rational Expressions and Equations3h 13m

Simplifying Rational Expressions
39m

Multiplying and Dividing Rational Expressions
25m

Adding and Subtracting Rational Expressions with Common Denominators
19m

Least Common Denominators
32m

Adding and Subtracting Rational Expressions with Different Denominators
32m

Rational Equations
44m

9. Inequalities and Absolute Value2h 52m

Set Operations and Compound Inequalities
42m

Absolute Value Equations
38m

Absolute Value Inequalities
39m

Linear Inequalities in Two Variables
28m

Systems of Linear Inequalities
23m

10. Relations and Functions2h 9m

Introduction to Relations and Functions
57m

Function Notation
15m

Graphing Common Functions
5m

Composition of Functions
24m

Direct & Inverse Variation
27m

11. Roots, Radicals, and Complex Numbers3h 57m

Introduction to Radical Expressions
47m

Simplifying Radical Expressions
47m

Adding and Subtracting Radicals
19m

Multiplying, Dividing, and Rationalizing Radicals
53m

Introduction to Complex Numbers
18m

Multiplying and Dividing Complex Numbers
51m

12. Quadratic Equations and Functions3h 1m

The Square Root Property
25m

Completing the Square
26m

The Quadratic Formula
40m

Graphing Quadratic Equations
1h 28m

13. Inverse, Exponential, & Logarithmic Functions2h 31m

Introduction to Inverse Functions
25m

Exponential Functions
35m

Introduction to Logarithmic Functions
33m

Properties of Logarithms
55m

14. Conic Sections & Systems of Nonlinear Equations2h 24m

Graphing Circles
32m

Ellipses
35m

Parabolas
35m

Hyperbolas
41m

15. Sequences, Series, and the Binomial Theorem1h 45m

Introduction to Sequences
40m

Arithmetic Sequences
27m

Geometric Sequences
26m

Factorials
11m

4. Graphing Linear Equations in Two Variables

Slope-Intercept Form

Beginning & Intermediate Algebra

4. Graphing Linear Equations in Two Variables

Slope-Intercept Form

Problema precedenteProssimo problema

Difficoltà con Beginning & Intermediate Algebra?

Unisciti a migliaia di studenti che si affidano a noi per superare al meglio i loro esami!

Scelta multipla

Graph the line represented by the equation $y = - \frac{4}{5} x + 2$

Graph of the line y = -4/5 x + 2 with plotted points at (0,2) and (5,-2) on a labeled coordinate plane.

Graph of the line y = -4/5 x + 2 with points at (0,2) and (-5,6) on a labeled xy-coordinate plane.

Graph of the line y = -4/5 x + 2 with points at (0,2) and (5,-2) on a labeled coordinate plane.

Graph of the line y = -4/5 x + 2 with plotted points and a downward sloping purple line on a grid.

0 Commenti

Problema precedenteProssimo problema

Guida verificata passo dopo passo

Identify the equation of the line given: $y = -\frac{4}{5}x + 2$. This is in slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Locate the y-intercept $b = 2$ on the graph. This is the point where the line crosses the y-axis, so plot the point $(0, 2)$.

Use the slope $m = -\frac{4}{5}$ to find another point. The slope means that for every 5 units you move to the right (positive direction on the x-axis), you move 4 units down (negative direction on the y-axis). Starting from $(0, 2)$, move right 5 units to $x=5$ and down 4 units to find the point $(5, -2)$.

Plot the second point $(5, -2)$ on the graph. This confirms the direction and steepness of the line.

Draw a straight line through the points $(0, 2)$ and $(5, -2)$ extending across the graph. This line represents the equation $y = -\frac{4}{5}x + 2$.