Answer:
The equation of the line is y = -2x + 7
Explanation:
* Lets study how to make an equation of the line from two point
- If the line passes through points (x1 , y1) and (x2 , y2)
- The form of the equation is y = mx + c, where m is the slope of the
line and c is the y-intercept
- The rule of the slope is m = (y2 - y1)/(x2 - x1)
- The y-intercept means the line intersect the y-axis at point (0 ,c)
* Now lets solve the problem
∵ The line passes through points (-3 , 13) and (4 , -1)
- Let (-3 , 13) is (x1 , y1) and (4 , -1) is (x2 , y2)
∵ m = (y2 - y1)/(x2 - x1)
∴ m = (-1 - 13)/(4 - -3)
∴ m = (-14)/7 = -2
- Lets write the form of the equation
∵ y = mx + c ⇒ substitute the value of m
∴ y = -2x + c
- To find the value of c use one of the two points to substitute the
values of x and y in the equation
∵ The line passes through (4 , -1)
∴ -1 = -2(4) + c
∴ -1 = -8 + c ⇒ add 8 to both sides
∴ -1 + 8 = -8 + 8 + c
∴ 7 = c
∴ y = -2x + 7
* The equation of the line is y = -2x + 7