QuestionAugust 24, 2025

10. A straight line passes through P(7,23) and R(-4,1) Find the equation of the line in the form ay+bx+c=0

10. A straight line passes through P(7,23) and R(-4,1) Find the equation of the line in the form ay+bx+c=0
10. A straight line passes through P(7,23) and R(-4,1) Find the equation of the line in the form ay+bx+c=0

Solution
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Answer

-2x + y - 9 = 0 Explanation 1. Calculate the slope Use **m = \frac{y_2 - y_1}{x_2 - x_1}**. Here, m = \frac{1 - 23}{-4 - 7} = \frac{-22}{-11} = 2. 2. Use point-slope form The equation is y - y_1 = m(x - x_1). Substitute m = 2, (x_1, y_1) = (7, 23): y - 23 = 2(x - 7). 3. Simplify to slope-intercept form Expand: y - 23 = 2x - 14. Rearrange: y = 2x + 9. 4. Convert to standard form Rearrange y = 2x + 9 to -2x + y - 9 = 0.

Explanation

1. Calculate the slope<br /> Use **$m = \frac{y_2 - y_1}{x_2 - x_1}$**. Here, $m = \frac{1 - 23}{-4 - 7} = \frac{-22}{-11} = 2$.<br /><br />2. Use point-slope form<br /> The equation is $y - y_1 = m(x - x_1)$. Substitute $m = 2$, $(x_1, y_1) = (7, 23)$: $y - 23 = 2(x - 7)$.<br /><br />3. Simplify to slope-intercept form<br /> Expand: $y - 23 = 2x - 14$. Rearrange: $y = 2x + 9$.<br /><br />4. Convert to standard form<br /> Rearrange $y = 2x + 9$ to $-2x + y - 9 = 0$.
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