Graphing - GED Math

1. Which quadrant contains the point $(-3, 4)$?

   Quadrant II. A negative $x$ and positive $y$ place it upper left.

2. What is the slope of the line through $(2, 1)$ and $(5, 7)$?

   $2$. $\frac{7 - 1}{5 - 2} = \frac{6}{3} = 2$.

3. What is the equation of the line with slope $2$ through $(1, 3)$, in slope-intercept form?

   $y = 2x + 1$. From $y - 3 = 2(x - 1)$, so $y = 2x - 2 + 3$.

4. What happens to the graph of $y = mx + b$ when only $b$ changes?

   The line shifts up or down by the change in $b$. The slope stays the same, so the new line is parallel.

5. What is the formula for the slope of a line through two points?

   $m = \frac{y_2 - y_1}{x_2 - x_1}$: the change in $y$ divided by the change in $x$.

6. How are the slopes of two parallel lines related?

   They are equal. Parallel lines have the same slope and different $y$-intercepts.

7. In slope-intercept form $y = mx + b$, what do $m$ and $b$ represent?

   $m$ is the slope and $b$ is the $y$-intercept, where the line crosses the $y$-axis.

8. What is the slope of a line perpendicular to $y = \frac{2}{3}x + 1$?

   $-\frac{3}{2}$. Flip the slope $\frac{2}{3}$ and change its sign.

9. What is the slope of a vertical line such as $x = 4$?

   Undefined. The run is $0$, and division by $0$ is undefined.

10. What is the $x$-intercept of $2x + 3y = 12$?

    $6$, the point $(6, 0)$. Set $y = 0$: $2x = 12$.

11. What is the slope of a horizontal line such as $y = 4$?

    $0$. The $y$ value never changes, so the rise is $0$.

12. How are the slopes of two perpendicular lines related?

    They are negative reciprocals: their product is $-1$, as with $2$ and $-\frac{1}{2}$.

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