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Lesson Topics Discussion Quiz: Class Homework

Example1

Title: Slope & Line Segment

Grade Lesson s4-l4

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

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)\$

Explanation:

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

Step: 2

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

Explanation:

To find the coordinates of the given points, (1, -2) and (4, -5), we can input them into the equation and determine that the slope is -1.

Step: 3

In this step, Use the point-slope form. Now that we have the slope (m = -1) and one point (1, -2), we can write the equation of the line: \$y − y_1 = m(x − x_1)\$

⇒y - (-2) = -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 - (-2) = -1(x - 1).

Step: 4

Let’s move on to the next step, where we’ll convert the equation to slope-intercept form (y = mx + b), with "b" representing the y-intercept. Here’s the simplified equation: y = -x + 1 - 2. After further simplification, we get: y = -x - 1

Explanation:

Convert the equation to slope-intercept form, y=mx+b, where "b" is the y-intercept. The simplified equation is y = - x - 1.

Step: 5

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.