Write the equation of the line in slope-intercept form that has slope 3 and passes through  
(
2
,
−
5
)
(2,−5).
slope: 
m
=
y
2
−
y
1
x
2
−
x
1
m= 
x 
2
​	
 −x 
1
​	
 
y 
2
​	
 −y 
1
​	
 
​	
            Point-slope: 
y
−
y
1
=
m
(
x
−
x
1
)
y−y 
1
​	
 =m(x−x 
1
​	
 )           Slope-intercept: 
y
=
m
x
+
b
y=mx+b 

To find the equation of a line in slope-intercept form (which is \( y = mx + b \)), we are given:

- The slope \( m = 3 \)
- A point \( (2, -5) \) through which the line passes.

### Step 1: Use the point-slope form equation
The point-slope form of a line is:

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

Substitute \( m = 3 \), \( x_1 = 2 \), and \( y_1 = -5 \):

\[
y - (-5) = 3(x - 2)
\]

Simplify:

\[
y + 5 = 3(x - 2)
\]

### Step 2: Expand and solve for \( y \)
Now, distribute the slope \( 3 \) on the right side:

\[
y + 5 = 3x - 6
\]

Subtract \( 5 \) from both sides to solve for \( y \):

\[
y = 3x - 6 - 5
\]

\[
y = 3x - 11
\]

### Final Answer:
The equation of the line in slope-intercept form is:

\[
y = 3x - 11
\]

Would you like more details on any step or have questions about the process?

---

Here are five related questions you might find helpful:

1. How do you calculate the slope when given two points?
2. What is the significance of the y-intercept in a line equation?
3. How do you convert from point-slope form to slope-intercept form?
4. Can you derive the equation of a horizontal line through a given point?
5. How does the slope value affect the steepness of the line?

**Tip:** When solving for the y-intercept \( b \), plugging a point into the slope-intercept equation \( y = mx + b \) can be a quick method!

Write the equation of the line in slope-intercept form that has slope 3 and passes through (2, −5).

Learn how to write the equation of a line with slope 3 passing through the point (2, -5). This problem demonstrates how to use the point-slope and slope-intercept forms to derive the final equation y = 3x - 11. Suitable for students in Grades 8-10.

Math Problem Statement

Write the equation of the line in slope-intercept form that has slope 3 and passes through
( 2 , − 5 ) (2,−5). slope: m

Point-slope: y − y 1

m ( x − x 1 ) y−y 1 =m(x−x 1 ) Slope-intercept: y

Solution

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