Math Problem Statement

Graph the line with the equation y, equals, minus, one fifth, x, plus, 4y=− 5 1 ​ x+4.

Graph the line with the equation y = -1/5x + 4.

Solution

The equation you provided is y=15x+4y = -\frac{1}{5}x + 4.

Let's break this down:

  1. The slope of the line is 15-\frac{1}{5}. This means that for every 5 units you move to the right along the x-axis, you move 1 unit down along the y-axis.
  2. The y-intercept is 4. This means the line crosses the y-axis at y=4y = 4.

Steps to graph:

  1. Start by plotting the y-intercept at the point (0,4)(0, 4).
  2. From this point, use the slope 15-\frac{1}{5}. Move 5 units to the right (positive direction on the x-axis), then 1 unit down (negative direction on the y-axis). This gives you a second point at (5,3)(5, 3).
  3. You can also move 5 units to the left (negative x-direction) and 1 unit up (positive y-direction) to get another point at (5,5)(-5, 5).

Connect these points with a straight line, and you will have the graph of y=15x+4y = -\frac{1}{5}x + 4.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Slope-Intercept Form

Formulas

y = mx + b (Slope-Intercept Form)
Slope = -1/5
y-intercept = 4

Theorems

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Suitable Grade Level

Grades 8-10