Question

graph this line:
y - 3 = -4(x - 7)
click to select points on the graph.
(graph with grid, axes, and a green line; points at (-9,9) and (5,-5) approximately, and the line passes through the origin? wait, no, lets parse the equation. the equation is point - slope form: y - y1 = m(x - x1), so point (7,3) with slope - 4. but the graph shown has a line, maybe the user is to graph the line from the equation, using the graph provided to click points. the ocr text is as above, with the equation and the graph instructions.)

Explanation:

Step1: Identify point from point-slope form

The equation $y - 3 = -4(x - 7)$ is in point-slope form $y-y_1=m(x-x_1)$, so one point is $(7, 3)$.

Step2: Convert to slope-intercept form

Expand and simplify to find $y$:

$$\begin{align*} y - 3 &= -4x + 28\\ y &= -4x + 31 \end{align*}$$

Step3: Find a second point

Set $x=0$, calculate $y$:
$y = -4(0) + 31 = 31$ (too large for graph). Instead, use $x=5$:
$y = -4(5) + 31 = 11$ (still large). Use $x=8$:
$y = -4(8) + 31 = -1$, so point $(8, -1)$.
Or use the slope $m=-4$: from $(7,3)$, move 1 right, 4 down to $(8, -1)$; move 1 left, 4 up to $(6, 7)$.

Step4: Verify graph points

The given graph has points $(-9, 9)$ and $(5, -5)$: check if they fit the line:
For $(-9,9)$: $9-3=-4(-9-7) \to 6=-4(-16) \to 6=64$ (no, error). Correct points to plot are $(7, 3)$ and $(8, -1)$, or $(6, 7)$.

Answer:

To graph the line $y - 3 = -4(x - 7)$:

1. Plot the point $(7, 3)$ (from the point-slope form).
2. Use the slope $-4$: from $(7,3)$, move 1 unit right and 4 units down to plot $(8, -1)$, or 1 unit left and 4 units up to plot $(6, 7)$.
3. Draw a straight line through these points.

The correct points to select on the provided grid are $\boldsymbol{(7, 3)}$ and $\boldsymbol{(8, -1)}$ (or equivalent points on the line $y=-4x+31$).