What is the equation of the line parallel to x = 7, passing through the point (-4, 1)? a. x = -4 b. x = 1 c. y = -4 d. y = 1

Option A

The equation of the line parallel to x = 7, passing through the point (-4, 1) is x = -4

Solution:

Given that the line is parallel to x = 7 and passes through the point (-4, 1)

we have to find the equation of the line.

Step 1:

x=7 is the equation of a vertical line parallel to the y-axis.

Thus a parallel line will have equation x = c

Where c is the value of the x- coordinate the line passes through.

Step 2:

The line passes through (- 4, 1) with x- coordinate of - 4, thus

x = - 4 is the equation of the parallel line.

Result:

Thus the equation of the line parallel to x = 7, passing through the point (-4, 1) is -4.

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form