Answer:
The equation of the line is y = [tex]-\frac{4}{5}[/tex] x + [tex]\frac{3}{5}[/tex]
Step-by-step explanation:
The form of the linear equation is y = m x + b, where
The rule of the slope is m = [tex]\frac{y2-y1}{x2-x1}[/tex] , where
- (x1, y1) and (x2, y2) are two points on the line
∵ A line passes through points (2, -1) and (-3, 3)
∴ x1 = 2 ad y1 = -1
∴ x2 = -3 and y2 = 3
→ Use the rule of the slope above to find the slope of the line
∵ m = [tex]\frac{3--1}{-3-2}[/tex] = [tex]\frac{3+1}{-5}[/tex] = [tex]\frac{4}{-5}[/tex]
∴ m = [tex]-\frac{4}{5}[/tex]
→ Substitute the value of m in the form of the equation above
∴ y = [tex]-\frac{4}{5}[/tex] x + b
→ To find b substitute x and y in the equation by the coordinates of one
point of the given points
∵ x = 2 and y = -1
∴ -1 = [tex]-\frac{4}{5}[/tex] (2) + b
∴ -1 = [tex]-\frac{8}{5}[/tex] + b
→ Add [tex]\frac{8}{5}[/tex] t both sides
∵ -1 + [tex]\frac{8}{5}[/tex] = b
∴ [tex]\frac{3}{5}[/tex] = b
→ Substitute the value of b in the equation
∴ y = [tex]-\frac{4}{5}[/tex] x + [tex]\frac{3}{5}[/tex]
∴ The equation of the line is y = [tex]-\frac{4}{5}[/tex] x + [tex]\frac{3}{5}[/tex]
