Question
Part 1 of 2 Write the point-slope form of the line satisfying the given conditions. Then use the point-slope form of the equation to write the slope-intercept form of the equation. Passing through \( (4,8) \) and \( (7,14) \) Type the point-slope form of the equation of the line. (Simplify your answer. Use integers or fractions for any number in the equation.)
Ask by Brooks Crawford. in the United States
Feb 26,2025
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Tutor-Verified Answer
Answer
The point-slope form of the equation is \( y - 8 = 2(x - 4) \). The slope-intercept form is \( y = 2x \).
Solution
Step 1: Find the slope (m) using the two points (4, 8) and (7, 14).
m = (14 - 8) / (7 - 4) = 6 / 3 = 2
Step 2: Use the point-slope form of a line, y - y₁ = m(x - x₁). Using the point (4, 8):
y - 8 = 2(x - 4)
This is the point-slope form.
Step 3: To write the slope-intercept form, expand and simplify:
y - 8 = 2x - 8
y = 2x - 8 + 8
y = 2x
So, the slope-intercept form of the equation is y = 2x.
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Simplify this solution Mind Expander
To find the point-slope form of the line, we first need to determine the slope \( m \). The slope can be calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the points \( (4,8) \) and \( (7,14) \): \[ m = \frac{14 - 8}{7 - 4} = \frac{6}{3} = 2 \] Now that we have the slope, we can use the point-slope form equation, which is: \[ y - y_1 = m(x - x_1) \] Using point \( (4,8) \): \[ y - 8 = 2(x - 4) \] Now, to write it in slope-intercept form \( y = mx + b \), we simplify: \[ y - 8 = 2x - 8 \\ y = 2x \] So the point-slope form of the equation is \( y - 8 = 2(x - 4) \) and the slope-intercept form is \( y = 2x \).
