To graph the line [tex]\( y = -\frac{3}{4}(x+1)-5 \)[/tex], we'll first find two points on the line. These points will be used to accurately plot the line on the graph.
1. Choose two x-values:
- Let's select [tex]\( x = 0 \)[/tex] and [tex]\( x = 4 \)[/tex]. These values make calculations straightforward.
2. Calculate the corresponding y-values:
- For [tex]\( x = 0 \)[/tex]:
[tex]\[
y = -\frac{3}{4}(0 + 1) - 5 = -\frac{3}{4}(1) - 5 = -\frac{3}{4} - 5 = -0.75 - 5 = -5.75
\][/tex]
So, the coordinates are [tex]\( (0, -5.75) \)[/tex].
- For [tex]\( x = 4 \)[/tex]:
[tex]\[
y = -\frac{3}{4}(4 + 1) - 5 = -\frac{3}{4}(5) - 5 = -3.75 - 5 = -8.75
\][/tex]
Thus, the coordinates are [tex]\( (4, -8.75) \)[/tex].
3. Plot the points on the graph:
- The first point is [tex]\( (0, -5.75) \)[/tex].
- The second point is [tex]\( (4, -8.75) \)[/tex].
4. Draw the line:
- Using these two points, draw a straight line that extends in both directions on the graph.
By following these steps, you should be able to accurately graph the line [tex]\( y = -\frac{3}{4}(x+1)-5 \)[/tex].
