Problem Analysis:
The image provides a cheat sheet for understanding the equation of a line in slope-intercept form, \( y = mx + b \). Here's what we know from the image:
1.
Slope (\( m \)): Represents the rate of change of the line.
2.
y-intercept (\( b \)): The point where the line crosses the y-axis.
The task is to identify the slope and y-intercept from the given equation:
\[ y = -3x + 5 \]
Step-by-Step Solution:
#### 1. Recall the Slope-Intercept Form:
The general form of a linear equation is:
\[ y = mx + b \]
where:
- \( m \) is the slope.
- \( b \) is the y-intercept.
#### 2. Compare the Given Equation with the General Form:
The given equation is:
\[ y = -3x + 5 \]
By comparing this with the general form \( y = mx + b \):
- The coefficient of \( x \) is \( -3 \). This corresponds to the slope \( m \).
- The constant term is \( 5 \). This corresponds to the y-intercept \( b \).
#### 3. Identify the Slope and y-Intercept:
From the comparison:
- The slope (\( m \)) is \( -3 \).
- The y-intercept (\( b \)) is \( 5 \).
#### 4. Fill in the Blanks:
The task asks us to fill in the blanks for the slope and y-intercept in the equation \( y = -3x + 5 \):
- The slope of the line is \( -3 \).
- The y-intercept is \( 5 \).
Final Answer:
\[
\boxed{-3, 5}
\]
Parent Tip: Review the logic above to help your child master the concept of linear graph sheet.
