Math Problem Statement

A linear function is given. Complete parts​ (a)-(d). f left parenthesis x right parenthesis equals negative 3 x plus 4 Question content area bottom left Part 1 ​(a) Determine the slope and​ y-intercept of the function. The slope is

enter your response here.

Solution

For the linear function f(x)=3x+4f(x) = -3x + 4, the general form is:

f(x)=mx+bf(x) = mx + b

Where:

  • mm is the slope.
  • bb is the y-intercept.

In your function:

  • m=3m = -3 (slope),
  • b=4b = 4 (y-intercept).

So, the slope is -3 and the y-intercept is 4.

Would you like me to assist with parts (b)-(d), or offer more details on how slope and y-intercept are determined?

Here are 5 related questions to consider:

  1. How can you graph a linear function using its slope and y-intercept?
  2. What happens to the graph when the slope changes but the y-intercept stays the same?
  3. How do you find the x-intercept of a linear function?
  4. Can a linear function have a slope of zero? What does that mean graphically?
  5. What is the significance of a negative slope in a linear function?

Tip: The y-intercept tells you where the graph crosses the y-axis, while the slope determines how steep the line is!

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Math Problem Analysis

Mathematical Concepts

Linear Functions
Slope-Intercept Form
Graphing Functions

Formulas

Slope-intercept form: f(x) = mx + b

Theorems

Slope-intercept theorem

Suitable Grade Level

Grades 8-10