Write the equation of the line that passes through the points left parenthesis, 4, comma, minus, 3, right parenthesis(4,−3) and left parenthesis, minus, 5, comma, 4, right parenthesis(−5,4). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

To find the equation of a line passing through two points, we can use the **point-slope form** of a line equation:

\[
y - y_1 = m(x - x_1)
\]

Where:
- \((x_1, y_1)\) is one of the points the line passes through.
- \(m\) is the slope of the line.

### Step 1: Calculate the slope (m)
The slope formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substitute the coordinates of the given points \((4, -3)\) and \((-5, 4)\):

\[
m = \frac{4 - (-3)}{-5 - 4} = \frac{4 + 3}{-5 - 4} = \frac{7}{-9} = -\frac{7}{9}
\]

### Step 2: Write the point-slope form of the equation
We can use either of the two points for \((x_1, y_1)\). Let's use \((4, -3)\):

\[
y - (-3) = -\frac{7}{9}(x - 4)
\]

Simplifying:

\[
y + 3 = -\frac{7}{9}(x - 4)
\]

This is the equation of the line in point-slope form.

Would you like further clarification on any step?

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Here are five related questions:
1. How do you convert this equation to slope-intercept form?
2. What is the significance of the slope value in a line?
3. Can you find the equation of a line parallel to this one passing through a different point?
4. How do you determine if two lines are perpendicular using their slopes?
5. What are vertical and horizontal lines' equations in point-slope form?

**Tip:** Always simplify the slope calculation first to avoid errors when substituting into the equation!

Write the equation of the line that passes through the points (4,−3) and (−5,4). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

Learn how to write the equation of a line passing through the points (4,−3) and (−5,4) in fully simplified point-slope form. This problem explores algebraic concepts and coordinate geometry. Suitable for students in Grades 8-10.

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