Findthelineequation(secantline)passingthru(7,3)&(5,-3)

To find the equation of the secant line passing through the points \((7, 3)\) and \((5, -3)\), we can follow these steps:

### Step 1: Find the slope of the line
The slope \(m\) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting the coordinates of the points \((7, 3)\) and \((5, -3)\):

\[
m = \frac{-3 - 3}{5 - 7} = \frac{-6}{-2} = 3
\]
So, the slope of the line is \(m = 3\).

### Step 2: Use point-slope form to find the equation of the line
The point-slope form of a line equation is:
\[
y - y_1 = m(x - x_1)
\]
Using the point \((7, 3)\) and the slope \(m = 3\), we substitute into the formula:

\[
y - 3 = 3(x - 7)
\]
Simplifying:
\[
y - 3 = 3x - 21
\]
\[
y = 3x - 21 + 3
\]
\[
y = 3x - 18
\]

### Final Answer:
The equation of the secant line passing through \((7, 3)\) and \((5, -3)\) is:
\[
y = 3x - 18
\]

Would you like more details, or do you have any questions?

Here are 5 related questions you can explore:
1. How do you find the equation of a line when given only one point and a slope?
2. What is the relationship between parallel lines in terms of their slopes?
3. Can you explain how to convert the point-slope form to slope-intercept form?
4. How do you determine the x-intercept and y-intercept from a line equation?
5. What does the slope of a line tell us about the direction of the line?

**Tip:** The slope of a line is a measure of how steep the line is, and it tells you how much the \(y\)-value changes for each unit increase in \(x\).

Find the line equation (secant line) passing through (7, 3) & (5, -3)

Learn how to find the equation of a secant line passing through the points (7, 3) and (5, -3). This problem involves calculating the slope using the slope formula and applying the point-slope form to derive the final equation. Ideal for students in Grades 8-10.

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