Ch. 2 - Functions and Graphs

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo

Blitzer 8th Edition

Ch. 2 - Functions and Graphs

Problema 84

Capitolo 3, Problema 84

If one point on a line is (2, −6) and the line's slope is -3/2, find the y-intercept.

Guida verificata passo dopo passo

Recall the slope-intercept form of a line: $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Substitute the given slope $m = -\frac{3}{2}$ into the equation: $y = -\frac{3}{2}x + b$.

Use the given point $(2, -6)$ by substituting $x = 2$ and $y = -6$ into the equation: $-6 = -\frac{3}{2} \times 2 + b$.

Simplify the multiplication on the right side: $-6 = -3 + b$.

Solve for $b$ by adding 3 to both sides: $b = -6 + 3$.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.

Durata del video:

58s

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Slope of a Line

The slope measures the steepness and direction of a line, defined as the ratio of the change in y to the change in x between two points. It is often represented as 'm' and is crucial for writing the equation of a line.

Video consigliato:

06:49

The Slope of a Line

Slope-Intercept Form of a Line

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. This form allows easy identification of the line's slope and where it crosses the y-axis, facilitating the calculation of unknown parameters.

Video consigliato:

02:35

Graphing Lines in Slope-Intercept Form

Using a Point to Find the Y-Intercept

Given a point (x, y) on the line and the slope m, substitute these values into y = mx + b to solve for b, the y-intercept. This method uses known information to find the line's vertical intercept.

Video consigliato:

04:27

Finding Equations of Lines Given Two Points

Pratica correlata

Domanda del libro di testo

In Exercises 77–92, use the graph to determine a. the function's domain; b. the function's range; c. the x-intercepts, if any; d. the y-intercept, if any; and e. the missing function values, indicated by question marks, below each graph.

899

views

Domanda del libro di testo

152

views

Domanda del libro di testo

Begin by graphing the absolute value function, f(x) = |x|. Then use transformations of this graph to graph the given function. g(x) = |x+3|

837

views

Domanda del libro di testo

Use the graphs of f and g to solve Exercises 83–90.

Find (f+g)(−3).