Questions: A line passes through the point (8,3) and has a slope of 5/4. Write an equation in slope-intercept form for this line.

A line passes through the point (8,3) and has a slope of 5/4. Write an equation in slope-intercept form for this line.
Transcript text: A line passes through the point $(8,3)$ and has a slope of $\frac{5}{4}$. Write an equation in slope-intercept form for this line.
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Solution

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Solution Steps

Step 1: Start with the point-slope form of the equation

The point-slope form is $y - y_1 = m(x - x_1)$, where $(x_1, y_1) = (8, 3)$ and $m = 1.25$.

Step 2: Rearrange the equation to slope-intercept form

Rearranging the equation to solve for $y$, we get $y = mx + b$. To find $b$, we substitute the given values into the equation.

Step 3: Calculate the y-intercept ($b$)

Substituting $x_1 = 8$, $y_1 = 3$, and $m = 1.25$ into the equation, we get $b = y_1 - m \cdot x_1 = 3 - 1.25 \cdot 8 = -7$.

Final Answer:

The equation of the line in slope-intercept form is $y = 1.25x - 7$.

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