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 ____________ .
Find the slope and intercept of each line, and then write the slope-intercept
formula for the line.
3. $m = ________ b = ____$
4. $Y = __________________$
5. $m = ________ b = ____$
6. $Y = __________________$
7. $m = ________ b = ____$
8. $Y = __________________$
9. $m = ________ b = ____$
10. $Y = __________________$
Graph top-left: line with positive slope passing through the points $(-5, 1)$ and $(0, 4)$, position_hint=top-left.
Graph top-right: line with negative slope passing through the points $(-4, 2)$ and $(3, -3)$, position_hint=top-right.
Graph bottom-left: line with negative slope passing through the points $(-4, 3)$ and $(2, 0)$, position_hint=bottom-left.
Graph bottom-right: line with positive slope passing through the points $(-3, -4)$ and $(0, 4)$, position_hint=bottom-right.
1. The problem asks to find the slope in the formula $Y = 4X + 5$.
2. The problem asks to find the Y-intercept in the formula $Y = -X + 3$.
3-10. Find slope $m$ and intercept $b$ for lines passing through given points and write the slope-intercept form $Y = mX + b$.
---
### Step 1: Identify slope and intercept in given formulas
- For $Y = 4X + 5$, slope $m = 4$ and intercept $b = 5$.
- For $Y = -X + 3$, slope $m = -1$ (since $-X = -1 imes X$) and intercept $b = 3$.
### Step 2: Calculate slope $m$ for each pair of points using formula
$$m = \frac{y_2 - y_1}{x_2 - x_1}$$
### Step 3: Calculate intercept $b$ using formula
$$b = y - m x$$
where $(x,y)$ is one of the points.
---
### For top-left graph points $(-5,1)$ and $(0,4)$:
1. Calculate slope:
$$m = \frac{4 - 1}{0 - (-5)} = \frac{3}{5}$$
2. Calculate intercept using point $(0,4)$:
$$b = 4 - \frac{3}{5} \times 0 = 4$$
3. Equation:
$$Y = \frac{3}{5}X + 4$$
### For top-right graph points $(-4,2)$ and $(3,-3)$:
1. Calculate slope:
$$m = \frac{-3 - 2}{3 - (-4)} = \frac{-5}{7}$$
2. Calculate intercept using point $(-4,2)$:
$$b = 2 - \left(-\frac{5}{7}\right) \times (-4) = 2 - \frac{20}{7} = \frac{14}{7} - \frac{20}{7} = -\frac{6}{7}$$
3. Equation:
$$Y = -\frac{5}{7}X - \frac{6}{7}$$
### For bottom-left graph points $(-4,3)$ and $(2,0)$:
1. Calculate slope:
$$m = \frac{0 - 3}{2 - (-4)} = \frac{-3}{6} = -\frac{1}{2}$$
2. Calculate intercept using point $(-4,3)$:
$$b = 3 - \left(-\frac{1}{2}\right) \times (-4) = 3 - 2 = 1$$
3. Equation:
$$Y = -\frac{1}{2}X + 1$$
### For bottom-right graph points $(-3,-4)$ and $(0,4)$:
1. Calculate slope:
$$m = \frac{4 - (-4)}{0 - (-3)} = \frac{8}{3}$$
2. Calculate intercept using point $(0,4)$:
$$b = 4 - \frac{8}{3} \times 0 = 4$$
3. Equation:
$$Y = \frac{8}{3}X + 4$$
---
### Final answers:
1. Slope in $Y = 4X + 5$ is $4$.
2. Y-intercept in $Y = -X + 3$ is $3$.
3. $m = \frac{3}{5}$, $b = 4$
4. $Y = \frac{3}{5}X + 4$
5. $m = -\frac{5}{7}$, $b = -\frac{6}{7}$
6. $Y = -\frac{5}{7}X - \frac{6}{7}$
7. $m = -\frac{1}{2}$, $b = 1$
8. $Y = -\frac{1}{2}X + 1$
9. $m = \frac{8}{3}$, $b = 4$
10. $Y = \frac{8}{3}X + 4$