Graphing Linear Functions - Pre Algebra

1. What is the x-intercept of the graph of $y = 2x - 6$?

   $(3, 0)$. Setting $y = 0$ gives $2x = 6$, so $x = 3$.

2. Starting at the y-intercept of $y = \frac{3}{4}x + 1$, you move 4 units right. How many units up do you move to stay on the line?

   3 units up, reaching $(4, 4)$. A slope of $\frac{3}{4}$ means a rise of 3 for every run of 4.

3. Which way does the graph of a linear function with a negative slope go as you read from left to right?

   It falls (goes down). The $y$-values decrease as $x$ increases.

4. What is the y-intercept of the graph of $f(x) = -\frac{2}{3}x + 4$?

   $(0, 4)$. When $x = 0$, the $x$ term is 0 and $f(0) = 4$.

5. What is the rate of change of the linear function whose graph passes through $(-2, 7)$ and $(3, -8)$?

   $-3$. The slope is $\frac{-8 - 7}{3 - (-2)} = \frac{-15}{5} = -3$.

6. What is the least number of points needed to draw the graph of a linear function?

   Two. Exactly one straight line passes through any two distinct points.

7. Which point lies on the graph of $y = 3x + 1$: $(2, 7)$ or $(2, 6)$?

   $(2, 7)$, because $3(2) + 1 = 7$.

8. How do you find the x-intercept of a linear function from its equation?

   Set $y = 0$ and solve for $x$. The x-intercept is the point where the line crosses the x-axis.

9. What is the x-intercept of the graph of $y = -\frac{2}{3}x + 4$?

   $(6, 0)$. Setting $y = 0$ gives $\frac{2}{3}x = 4$, so $x = 6$.

10. What does the graph of $y = 5$ look like?

    A horizontal line through $(0, 5)$. Its slope is 0 because $y$ never changes.

11. A line has x-intercept $(-4, 0)$ and y-intercept $(0, 6)$. What is its slope?

    $\frac{3}{2}$. The slope is $\frac{6 - 0}{0 - (-4)} = \frac{6}{4} = \frac{3}{2}$.

12. What is the y-intercept of the graph of $y = mx + b$?

    The point $(0, b)$, where the line crosses the y-axis.

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