Math Problem Statement

find the equation using the formula y=mx+b

Find the equation of the line using the formula y = mx + b

Solution

To find the equation of the line in the form y=mx+by = mx + b, we need to determine two things:

  1. The slope mm of the line.
  2. The y-intercept bb, which is where the line crosses the y-axis.

Step 1: Find the slope mm

The slope mm is the "rise over run," which measures how steep the line is. The formula for the slope between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is:

m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1}

From the image, let's choose two points on the line. We can clearly see that:

  • One point is (4,1)(-4, -1) (left side of the graph).
  • Another point is (4,5)(4, 5) (right side of the graph).

Now, calculate the slope:

m=5(1)4(4)=5+14+4=68=34m = \frac{5 - (-1)}{4 - (-4)} = \frac{5 + 1}{4 + 4} = \frac{6}{8} = \frac{3}{4}

So, the slope m=34m = \frac{3}{4}.

Step 2: Find the y-intercept ( b

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Slope-Intercept Form

Formulas

y = mx + b
Slope formula: m = (y2 - y1) / (x2 - x1)

Theorems

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Suitable Grade Level

Grades 7-9