Answer:
[tex]y = -\frac{3}{7}x + 6[/tex]
Step-by-step explanation:
1. The slope-intercept form of any linear equation is y = mx + b, where y = y-coordinate, m = slope, x = x-coordinate, and b = y-intercept.
2. To find the slope from the two points (-7,9) and (7,3), we can use the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] and plug their values into the corresponding variable.
- [tex]\frac{3-9}{7-(-7)}[/tex]
- [tex]\frac{-6}{14}[/tex]
- [tex]-\frac{3}{7}[/tex]
3. Okay, great! We have our slope, so our equation should look like this so far: [tex]y = -\frac{3}{7}x + b[/tex]
4. To find b, the y-intercept, we can use the equation [tex]b = y_1 - m * x_1[/tex] and then plug in the values to their corresponding variable.
- [tex]b = 9 - (-\frac{3}{7}) * (-7)[/tex]
- [tex]b = 9 - \frac{21}{7}[/tex]
- [tex]b = 9 - 3[/tex]
- [tex]b = 6[/tex]
5. Now that we have our slope (-3/7) and y-intercept (6), we can plug in those values into m and b and get the equation: [tex]y = -\frac{3}{7}x + 6[/tex]
