Math Problem Statement

List the slope and​ y-intercept. Then, graph. ​f(x)equals3xminus5 Question content area bottom left Part 1 The slope is    enter your response here. ​(Simplify your​ answer.) Part 2 The​ y-intercept is    enter your response here. ​(Type an ordered pair. Simplify your​ answer.)

Solution

The equation of the function is given as:

f(x)=3x5f(x) = 3x - 5

Part 1: Slope

The function f(x)=3x5f(x) = 3x - 5 is in the slope-intercept form, which is:

y=mx+by = mx + b

where mm is the slope, and bb is the y-intercept.

  • Slope (m): The coefficient of xx is 3, so the slope is:

3\boxed{3}

Part 2: Y-intercept

The y-intercept is the value of f(x)f(x) when x=0x = 0. From the equation:

f(0)=3(0)5=5f(0) = 3(0) - 5 = -5

Thus, the y-intercept is:

(0,5)\boxed{(0, -5)}


Would you like me to help you graph the function?

Here are 5 additional related questions:

  1. How do you calculate the slope between two points?
  2. What does the slope tell you about the graph of a linear function?
  3. How do you find the x-intercept of a linear equation?
  4. How does changing the slope affect the steepness of the line?
  5. What are other forms of linear equations besides slope-intercept form?

Tip: To graph a line, plot the y-intercept first, then use the slope to determine other points.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Slope-Intercept Form
Graphing Functions

Formulas

Slope-Intercept Form: y = mx + b

Theorems

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Suitable Grade Level

Grades 8-10