Question

graph this line:
$y + 5 = -\frac{3}{4}(x + 5)$
click to select points on the grap

Explanation:

Step1: Identify the form

The equation \( y + 5 = -\frac{3}{4}(x + 5) \) is in point - slope form \( y - y_1=m(x - x_1) \), where \( (x_1,y_1)=(-5,-5) \) and \( m =-\frac{3}{4} \).

Step2: Plot the point

First, plot the point \( (-5,-5) \) on the coordinate plane.

Step3: Use the slope

The slope \( m =-\frac{3}{4} \) means that from the point \( (-5,-5) \), we can move down 3 units (because the numerator of the slope is - 3, indicating a decrease in the y - direction) and then move right 4 units (because the denominator of the slope is 4, indicating an increase in the x - direction), or move up 3 units and left 4 units.
For example, from \( (-5,-5) \), moving down 3 units gives \( y=-5 - 3=-8 \) and moving right 4 units gives \( x=-5 + 4=-1 \). So we get another point \( (-1,-8) \).
We can also rewrite the equation in slope - intercept form (\( y=mx + b \)) to find the y - intercept.
Start with \( y + 5=-\frac{3}{4}(x + 5) \)
Expand the right - hand side: \( y+5 =-\frac{3}{4}x-\frac{15}{4} \)
Subtract 5 from both sides: \( y=-\frac{3}{4}x-\frac{15}{4}-5 \)
Since \( 5=\frac{20}{4} \), then \( y =-\frac{3}{4}x-\frac{15 + 20}{4}=-\frac{3}{4}x-\frac{35}{4}=- \frac{3}{4}x-8.75 \)
The y - intercept is \( (0,-8.75) \), and we can also plot this point.
After plotting two or more points, we can draw a straight line through them to graph the line.

Answer:

To graph the line \( y + 5 = -\frac{3}{4}(x + 5) \), plot the point \( (-5,-5) \) (from the point - slope form) and use the slope \( -\frac{3}{4} \) to find additional points (e.g., \( (-1,-8) \) or \( (0,-8.75) \)) and then draw a straight line through the plotted points.