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Lesson Topics Discussion Quiz: Class Homework

Example1

Title: Geometry

Grade Lesson s4-p1

Explanation: The best way to understand PSAT-4 is by looking at some examples. Take turns and read each example for easy understanding.

Examples

Topics → Definition Example1 Example2 Example3

To find the equation of the line passing through the points (1, -2) and (4, -5).

Step: 1

First, to find the slope (m) of a line passing through two points \$(x_1, y_1)\$ and \$(x_2, y_2)\$ is given by: \$m = (y_2 - y_1)/(x_2 - x_1)\$.

Let’s plug in the coordinates of the given points (1, -2) and (4, -5): \$m = (-5 - (-2))/ (4 -1)\$ then \$m = (- 5 + 2)/ 3 = -1\$.

Explanation:

To find the slope (m) of a line passing through two points \$(x_1, y_1)\$ and \$(x_2, y_2)\$, you can use this formula: \$m = (y_2 - y_1) / (x_2 - x_1)\$.

Using the points (1, -2) and (4, -5), the slope(m) is -1.

Step: 2

In this step, the point-slope form of the equation of a line is: \$y - y_1 = m(x - x_1)\$.

Using the point (1,−2) and the slope m = −1:

⇒y - (-2) = -1(x - 1)

⇒ y + 2 = -1 (x) + 1

⇒ y = -1 (x) + 1 - 2

⇒ y = -1 (x) - 1

Explanation:

To proceed, apply the point-slope form. With the slope (m = -1) and one point (1, -2), we can formulate the equation of the line as follows: \$y − y_1 = m(x − x_1)\$. Therefore, substituting the values, we get y = -1x - 1.

Step: 3

So, the equation of the line passing through the points (1, -2) and (4, -5) is y = -x - 1.

Explanation:

The equation for the line that passes through the coordinates (1, -2) and (4, -5) is y = -x - 1.