To write the equation of the line in slope-intercept form (y = mx + b), we need to determine the slope (m) and the y-intercept (b) from the points (-4, -5) and (4, 5).
Step 1: Calculate the slope (m)
The formula for the slope between two points (x₁, y₁) and (x₂, y₂) is:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points (-4, -5) as (x₁, y₁) and (4, 5) as (x₂, y₂):
\[ m = \frac{5 - (-5)}{4 - (-4)} = \frac{5 + 5}{4 + 4} = \frac{10}{8} = \frac{5}{4} \]
Step 2: Use the slope to find the y-intercept (b)
Now that we have the slope, we can use one of the points to find the y-intercept. We can use the point (4, 5). The slope-intercept form is:
\[ y = mx + b \]
Substituting the known values:
\[ 5 = \frac{5}{4} \cdot 4 + b \]
Calculating \(\frac{5}{4} \cdot 4\):
\[ 5 = 5 + b \]
Solving for b:
\[ 5 - 5 = b \]
\[ b = 0 \]
Step 3: Write the equation
Now we can write the equation of the line in slope-intercept form:
\[ y = \frac{5}{4}x + 0 \]
Simplifying, we get:
\[ y = \frac{5}{4}x \]
Thus, the final answer is:
The equation in slope-intercept form is \(y = \frac{5}{4}x\).
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