Answer:
[tex]\[ y = \frac{{-5}}{{2}}x - 2 \][/tex]
Step-by-step explanation:
Choose two points from the graph. I will choose the two points (-2,3) and (0,-2). To find the equation of a line passing through the points (-2,3) and (0,-2), we'll follow these steps:
1. Find the slope m:
[tex]\[ m = \frac{{y_2 - y_1}}{{x_2 - x_1}} \][/tex]
Given the points (-2,3) and (0,-2), we have:
[tex]\[ m = \frac{{-2 - 3}}{{0 - (-2)}} = \frac{{-5}}{{2}} \][/tex]
2. Use one of the points to find the y-intercept b. Let's use the point (-2,3):
[tex]\[ 3 = \frac{{-5}}{{2}} \times (-2) + b \]\[ 3 = 5 + b \]\[ b = 3 - 5 \]\[ b = -2 \][/tex]
Now we have the slope [tex]\( m = \frac{{-5}}{{2}} \)\\[/tex] and the y-intercept [tex]\( b = -2 \)[/tex]. So, the equation of the line is:
[tex]\[ y = \frac{{-5}}{{2}}x - 2 \][/tex]
