Question: SYSTEMATIC REVIEW
Fill in the blanks.
1 A line that includes the point $(0, -3)$ has a Y-intercept of ____________.
2. A line with a negative slope slants ____________ to the right as $X$ increases.
Find the slope and intercept of each line, and then write the slope-intercept formula
for the line.
$B$=intercept
$Y= Mx + B$
3. $m = ________$ $b = ____$
4. $Y = __________________$
5. $m = ________$ $b = ____$
6. $Y = __________________$
7. $m = ________$ $b = ____$
8. $Y = __________________$
9. $m = ________$ $b = ____$
10. $Y = __________________$
graph top-left: a line with positive slope passes through $(0, -3)$ and $(3, 2)$, position_hint=top-left
graph top-right: a line with negative slope passes through $(0, 1)$ and $(3, 0)$, position_hint=top-right
graph center-left: a line with positive slope passes through $(0, 0)$ and $(5, 4)$, position_hint=center
graph bottom-right: a line with positive slope passes through $(-2, -2)$ and $(2, 0)$, position_hint=bottom-right
User: help me solve correctly
1. The Y-intercept is the $y$-value when $x=0$. Given the point $(0, -3)$, the Y-intercept is $-3$.
2. A line with a negative slope slants \textbf{downward} to the right as $x$ increases.
Now, find the slope $m$ and intercept $b$ for each line and write the slope-intercept form $Y = mx + b$.
3. For the line through $(0, -3)$ and $(3, 2)$:
$$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - (-3)}{3 - 0} = \frac{5}{3}$$
Since it passes through $(0, -3)$, $b = -3$.
4. Equation:
$$Y = \frac{5}{3}x - 3$$
5. For the line through $(0, 1)$ and $(3, 0)$:
$$m = \frac{0 - 1}{3 - 0} = \frac{-1}{3} = -\frac{1}{3}$$
Intercept $b = 1$ (since it passes through $(0,1)$).
6. Equation:
$$Y = -\frac{1}{3}x + 1$$
7. For the line through $(0, 0)$ and $(5, 4)$:
$$m = \frac{4 - 0}{5 - 0} = \frac{4}{5}$$
Intercept $b = 0$.
8. Equation:
$$Y = \frac{4}{5}x$$
9. For the line through $(-2, -2)$ and $(2, 0)$:
$$m = \frac{0 - (-2)}{2 - (-2)} = \frac{2}{4} = \frac{1}{2}$$
To find $b$, use point-slope form with point $(-2, -2)$:
$$-2 = \frac{1}{2}(-2) + b \Rightarrow -2 = -1 + b \Rightarrow b = -1$$
10. Equation:
$$Y = \frac{1}{2}x - 1$$