Chapter 13: Q. 24 (page 533)

A line with slope $- \frac{5}{2}$ passes through points (7, -4) and (?, 6).

Short Answer

Expert verified

A line with slope $- \frac{5}{2}$ passes through points $(7, - 4) and (3, 6)$

Step by step solution

Step-1 – Given

A line with slope $- \frac{5}{2}$ passes through points $(7, - 4) and (?, 6)$

Step-2 – To determine

We have tofind the unknownx coordinate of the given point.

Step-3 – Calculation

The slope formula for two points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ is:

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

The given points are $(7, - 4) and (?, 6)$ .

Let = the unknown x coordinate

So,

$\begin{array}{l} m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} \\ m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} \\ - \frac{5}{2} = \frac{6 - (- 4)}{x_{2} - 7} \\ - \frac{5}{2} = \frac{10}{x_{2} - 7} \\ - 5 (x_{2} - 7) = 20 \\ - 5 x_{2} + 35 = 20 \\ - 5 x_{2} = - 15 \\ x_{2} = 3 \end{array}$

Hence, the unknownx coordinate is 3.

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A line with slope $- \frac{5}{2}$ passes through points (7, -4) and (?, 6).

Short Answer

Step by step solution

Step-1 – Given

Step-2 – To determine

Step-3 – Calculation

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A line with slope−52 passes through points (7, -4) and (?, 6).

Short Answer

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A line with slope $- \frac{5}{2}$ passes through points (7, -4) and (?, 6).