Answer:
The slope is 3
The y-intercept is -2
The linear equation is y = 3x - 2
Explanation:
The form of the linear equation is y = m x + b, where
- m is the slope of the line
- The rule of the slope of a line that passes through points (x1, y1) and (x2, y2) is m =
∵ A line passes through points (2, 4) and (6, 16)
∴ x1 = 2 and y1 = 4
∴ x2 = 6 and y2 = 16
→ Substitute them in the rule of the slope above to find it
∵ m =
=
= 3
∴ m = 3
→ Substitute it in the form of the equation above
∴ y = 3x + b
→ To find b substitute x and y in the equation by the coordinates of
a point on the line
∵ Point (2, 4) is on the line
∴ x = 2 and y = 4
∵ 4 = 3(2) + b
∴ 4 = 6 + b
→ Subtract 6 from both sides to find b
∵ 4 - 6 = 6 - 6 + b
∴ -2 = b
→ Substitute its value on the equation above
∵ y = 3x + (-2)
∴ y = 3x - 2
→ Let us answer the questions
The slope is 3
The y-intercept is -2
The linear equation is y = 3x - 2