Answer:
1. The slope of the line is -2
2. The y-intercept is 10
3. The equation in slope-intercept form is y = -2x + 10
Step-by-step explanation:
The slop-intercept form of the linear equation is y = m x + b, where
- m is the slope of the line
- b is the y-intercept (value y at x = 0)
- The rule of the slope of the line using two points on the line (x1, y1) and (x2, y2) is m = [tex]\frac{y2-y1}{x2-x1}[/tex]
From the given table
∵ (2, 6) and (3, 4) are two points on the line
∴ x1 = 2 and y1 = 6
∴ x2 = 3 and y2 = 4
→ Substitute them in the rule of the slope above to find it
∵ m = [tex]\frac{4-6}{3-2}[/tex] = [tex]\frac{-2}{1}[/tex] = -2
∴ m = -2
∴ The slope of the line is -2 ⇒ (1)
→ Substitute it in the form of the equation above
∴ y = -2x + b
→ To find b substitute x and y in the equation by the coordinates of
any point in the table
∵ (5, 0) is a point on the table
∴ x = 5 and y = 0
∵ 0 = -2(5) + b
∴ 0 = -10 + b
→ Add 10 to both sides
∵ 0 + 10 = -10 + 10 + b
∴ 10 = b
∴ The y-intercept is 10 ⇒ (2)
→ Substitute the value of b in the equation
∵ y = -2x + 10
∴ The equation in slope-intercept form is y = -2x + 10 ⇒ (3)
