If ( -2, -5) are the coordinates of a point on a line that has slope 2, what is the y-coordinate of the point on the line at which x = -3

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We can use the **point-slope form** of a linear equation to find the y-coordinate of the point on the line when \( x = -3 \).

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

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

Where:
- \( (x_1, y_1) \) is a known point on the line, in this case \( (-2, -5) \),
- \( m \) is the slope of the line, which is given as \( 2 \),
- \( (x, y) \) is the point we want to find on the line when \( x = -3 \).

### Step 2: Substitute the known values into the formula
We know that the slope \( m = 2 \), and the point \( (-2, -5) \) lies on the line. So:

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

Simplifying:

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

### Step 3: Solve for \( y \) when \( x = -3 \)
Substitute \( x = -3 \) into the equation:

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

\[
y + 5 = 2(-1)
\]

\[
y + 5 = -2
\]

Now, subtract 5 from both sides to solve for \( y \):

\[
y = -2 - 5
\]

\[
y = -7
\]

### Final Answer:
The y-coordinate of the point when \( x = -3 \) is \( \boxed{-7} \).

Would you like further details or have any questions? Here are some related questions for you:

1. What is the equation of the line through the point \( (-2, -5) \) with slope 2?
2. How do you find the slope of a line when given two points?
3. How would the equation change if the slope were different?
4. What is the meaning of the point-slope form of a line in real-life situations?
5. How can you graph a line given a point and its slope?

Tip: When solving for a point on a line, always make sure to substitute the \( x \)-value into the equation correctly to avoid errors!

If (-2, -5) are the coordinates of a point on a line that has slope 2, what is the y-coordinate of the point on the line at which x = -3?

Discover how to find the y-coordinate of a point on a line given the coordinates (-2, -5) and a slope of 2. Using the point-slope form, this solution is ideal for students in Grades 8-10 looking to strengthen their understanding of linear equations.

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