Question

graph the equation.

1. $y - 6 = 3(x - 4)$
2. $y + 1 = 2(x - 5)$
3. $y - 2 = -4(x + 3)$
4. $y + 2 = -(x - 1)$
5. $y = \frac{1}{2}(x - 5)$
6. $y + 3 = 5x$
7. $y + 1 = \frac{2}{3}(x + 1)$
8. $y - 2 = -\frac{1}{2}(x - 3)$
9. $y + \frac{1}{2} = 2(x - 1)$

Explanation:

Step1: Identify point-slope form

The equation $y + 3 = 5x$ can be rewritten as $y - (-3) = 5(x - 0)$, which matches the point-slope form $y - y_1 = m(x - x_1)$. Here, the point $(x_1, y_1)$ is $(0, -3)$ and slope $m=5$.

Step2: Plot the known point

Mark the point $(0, -3)$ on the coordinate grid; this is the y-intercept.

Step3: Use slope to find a second point

Slope $m=5=\frac{5}{1}$, meaning move 5 units up and 1 unit right from $(0, -3)$ to get the point $(1, 2)$.

Step4: Draw the line

Connect the points $(0, -3)$ and $(1, 2)$ with a straight line, extending it across the grid.

Answer:

The graph is a straight line passing through points $(0, -3)$ and $(1, 2)$, extending infinitely in both directions.