graph this line: y - 4 = -\\frac{1}{4}(x + 3) click to select points on the graph.

Explanation:

Step1: Identify the point - slope form

The equation $y - 4=-\frac{1}{4}(x + 3)$ is in point - slope form $y - y_1=m(x - x_1)$, where $(x_1,y_1)=(-3,4)$ and $m =-\frac{1}{4}$.

Step2: Find the y - intercept

Set $x = 0$: [ \begin{align*} y-4&=-\frac{1}{4}(0 + 3)\ y-4&=-\frac{3}{4}\ y&=4-\frac{3}{4}=\frac{16 - 3}{4}=\frac{13}{4}=3.25 \end{align*} ]

Step3: Find the x - intercept

Set $y = 0$: [ \begin{align*} 0-4&=-\frac{1}{4}(x + 3)\ -4&=-\frac{1}{4}(x + 3)\ x+3&=16\ x&=13 \end{align*} ]

Step4: Plot the points and draw the line

Plot the point $(-3,4)$ (from the point - slope form), the y - intercept $(0,3.25)$ and the x - intercept $(13,0)$ and draw a straight line through them.

Answer:

Graph the line by plotting the points $(-3,4)$, $(0,3.25)$ and $(13,0)$ and drawing a straight - line through them.