Question: Fill in the blanks. 1. In the formula $Y = 4X + 5$, the slope is ____________. 2. In the formula $Y = -X + 3$, the Y-intercept is ____________. 3. Parallel lines have the same ____________. For each graph, tell whether the slope is positive or negative, and then make a triangle and find $m$. 4. positive or negative? ______ m = ______ 5. positive or negative? ______ m = ______ Graph 4: line with negative slope, crossing the y-axis near the origin and passing through points approximately left-above and right-below; position_hint = center-left. Graph 5: line with positive slope, crossing near the origin and passing through points approximately left-below and right-above; position_hint = center-right.

1. **State the problem:** Fill in the blanks for slope, intercept, and properties of parallel lines. 2. **Recall formulas and definitions:** - The slope-intercept form of a line is $Y = mX + b$, where $m$ is the slope and $b$ is the Y-intercept. - Parallel lines have the same slope. 3. **Solve each blank:** **1.** Given $Y = 4X + 5$, the slope $m$ is the coefficient of $X$, so $m = 4$. **2.** Given $Y = -X + 3$, the Y-intercept $b$ is the constant term, so $b = 3$. **3.** Parallel lines have the same slope. 4. **Analyze Graph 4:** - The line has a negative slope (it goes down from left to right). - To find $m$, pick two points: approximate points are left-above $(x_1, y_1)$ and right-below $(x_2, y_2)$. - Suppose points are $( -1, 1 )$ and $( 1, -1 )$. - Calculate slope: $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1 - 1}{1 - (-1)} = \frac{-2}{2} = -1$$ 5. **Analyze Graph 5:** - The line has a positive slope (it goes up from left to right). - Approximate points: left-below $(x_1, y_1)$ and right-above $(x_2, y_2)$. - Suppose points are $( -1, -1 )$ and $( 1, 1 )$. - Calculate slope: $$m = \frac{1 - (-1)}{1 - (-1)} = \frac{2}{2} = 1$$ **Final answers:** 1. Slope is $4$. 2. Y-intercept is $3$. 3. Parallel lines have the same slope. 4. Negative; $m = -1$. 5. Positive; $m = 1$.