Question

Write an equation in standard form of the line that contains the point (-2,4) and is parallel to (has the same slope as) the line y = 8x-3.

Answer 1

Answer:

The equation of the line in standard form is -8x + y = 20

Step-by-step explanation:

The standard form of the linear equation is Ax + By = C, where

• A, B, and C are integers

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

• m is the slope

• b is the y-intercept

Parallel lines have equal slopes

∵ The line is parallel to the line y = 8x - 2

→ Compare it with the slope-intercept form above

∴ m = 8

∵ The parallel lines have the same slopes

∴ The slope of the line = 8

→ Substitute it in the slope-intercept form above

∴ y = 8x + b

∵ The line passes through the point (-2, 4)

∴ x = -2 and y = 4

→ Substitute x by -2 and y by 4 in the equation to find b

∵ 4 = 8(-2) + b

∴ 4 = -16 + b

→ Add 16 to both sides

∴ 4 + 16 = -16 + 16 + b

∴ 20 = b

→ Substitute the value of b in the equation above

∴ y = 8x + 20

→ Subtract both sides by 8x

∵ y - 8x = 8x - 8x + 20

∴ y - 8x = 20

→ Switch x and y

∴ -8x + y = 20

∴ The equation of the line in standard form is -8x + y = 20