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