Question

What are the answers here?

Answer 1

Answer:

The slope is 3

The y-intercept is -2

The linear equation is y = 3x - 2

Step-by-step explanation:

The form of the linear equation is y = m x + b, where

• m is the slope of the line

• b is the y-intercept

• The rule of the slope of a line that passes through points (x1, y1) and (x2, y2) is m = $\frac{y2-y1}{x2-x1}$

∵ 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 = $\frac{16-4}{6-2}$ = $\frac{12}{4}$ = 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