Write an equation in slope-intercept form for the linear function that goes through the points (3. -4). Don't use decimals in your equation. [b]
Write an equation in slope-intercept form for the linear function that goes through the points (3. -4). Don't use decimals in your equation. [b]
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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![**Question 13**
Write an equation in slope-intercept form for the linear function that goes through the points (3, -1) and (5, -4). Don't use decimals in your equation. [b]
**Explanation:**
To find the equation of the line in slope-intercept form (y = mx + b), we need to calculate the slope (m) using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substitute the given points (3, -1) and (5, -4) into the formula:
\[ m = \frac{-4 - (-1)}{5 - 3} = \frac{-4 + 1}{2} = \frac{-3}{2} \]
So, the slope \( m \) is \(-\frac{3}{2}\).
Next, use the point-slope form to find the y-intercept (b). Choose one point, for example, (3, -1):
\[ y - y_1 = m(x - x_1) \]
\[ -1 - (-1) = -\frac{3}{2}(x - 3) \]
Simplify and solve for b:
\[ -1 = -\frac{3}{2}(3) + b \]
\[ -1 = -\frac{9}{2} + b \]
\[ b = -1 + \frac{9}{2} = \frac{-2}{2} + \frac{9}{2} = \frac{7}{2} \]
Thus, the equation in slope-intercept form is:
\[ y = -\frac{3}{2}x + \frac{7}{2} \]
*Note: On many educational platforms, the exact requirement is to use fractions rather than decimals to represent numbers in the equation.*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F49c6a8b6-f23b-490b-9d51-bf62d89a59da%2F6f51c989-c632-449f-975a-129a52887682%2F886lu1g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 13**
Write an equation in slope-intercept form for the linear function that goes through the points (3, -1) and (5, -4). Don't use decimals in your equation. [b]
**Explanation:**
To find the equation of the line in slope-intercept form (y = mx + b), we need to calculate the slope (m) using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substitute the given points (3, -1) and (5, -4) into the formula:
\[ m = \frac{-4 - (-1)}{5 - 3} = \frac{-4 + 1}{2} = \frac{-3}{2} \]
So, the slope \( m \) is \(-\frac{3}{2}\).
Next, use the point-slope form to find the y-intercept (b). Choose one point, for example, (3, -1):
\[ y - y_1 = m(x - x_1) \]
\[ -1 - (-1) = -\frac{3}{2}(x - 3) \]
Simplify and solve for b:
\[ -1 = -\frac{3}{2}(3) + b \]
\[ -1 = -\frac{9}{2} + b \]
\[ b = -1 + \frac{9}{2} = \frac{-2}{2} + \frac{9}{2} = \frac{7}{2} \]
Thus, the equation in slope-intercept form is:
\[ y = -\frac{3}{2}x + \frac{7}{2} \]
*Note: On many educational platforms, the exact requirement is to use fractions rather than decimals to represent numbers in the equation.*
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