QuestionIn the figure, the coordinates of $P$ are A. $(-3,0)$ . B. $(-4,0)$ . C. $(-5,0)$ . D. $(-6,0)$ . D

Studdy Solution

STEP 1

1. The line passes through the points $(5, 6)$ and $(0, 3)$ .
2. The point $P$ is on the x-axis, meaning its coordinates are $(P, 0)$ .
3. We need to find the x-coordinate of point $P$ .

STEP 2

1. Find the equation of the line passing through the given points.
2. Determine where the line intersects the x-axis.
3. Identify the x-coordinate of the intersection point as the value of $P$ .

STEP 3

Find the slope of the line using the formula for slope $\frac{y_2 - y_1}{x_2 - x_1}$ :
Given points $(5, 6)$ and $(0, 3)$ :
$\text{slope} = \frac{3 - 6}{0 - 5} = \frac{-3}{-5} = \frac{3}{5}$

STEP 4

Use the point-slope form of a line equation $y - y_1 = m(x - x_1)$ with point $(0, 3)$ and slope $\frac{3}{5}$ :
$y - 3 = \frac{3}{5}(x - 0)$
Simplify the equation:
$y - 3 = \frac{3}{5}x$ $y = \frac{3}{5}x + 3$

STEP 5

To find the x-intercept, set $y = 0$ in the equation of the line:
$0 = \frac{3}{5}x + 3$
Solve for $x$ :
$-3 = \frac{3}{5}x$ $x = -3 \times \frac{5}{3}$ $x = -5$

STEP 6

The x-coordinate of point $P$ is $-5$ .
The coordinates of $P$ are:
$\boxed{(-5, 0)}$

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