Question

19 What is the equation in standard form of the line that passes through the point (6,-1) and is

parallel to the line represented by 8x + 3y = 15?
8x + 3y = -45
B 8x-3y = -51
C 8x + 3y = 45
D 8x-3y = 51

Answer 1

C. 8x + 3y = 45

Explanation:

Currently, the line we're given is in standard form, whose general form is

`Ax+By=C`

We know that parallel lines have the same slope (m), as

`m_(2)=m_(1)`, where m2 is the slope of the line we're trying to find and m1 is the slope of the line we're given.

We don't know the slope (m1) of the line we're already given while the line is in standard form, but we can find it by converting the line from standard form to slope-intercept form, whose general form is

`y=mx+b`, where m is the slope and b is the y-intercept.

To convert from standard form to slope-intercept form, we must simply isolate y on the left-hand side of the equation:

`8x+3y=15\\3y=-8x+15\\y=-8/3x+5`

Thus, the slope of the first line is -8/3 and the slope of the other line is also -8/3.

We can find the y-intercept of the other line by using the slope-intercept form and plugging in -8/3 for m, and (6, -1) for x and y:

`-1=-8/3(6)+b\\-1=-16+b\\15=b`

Thus, the equation of the line in slope-intercept form is y = -8/3x + 15

We can covert this into standard form, first by clearing the fraction (multiply both sides by 3) and isolate the constant made after multiplying both sides by 3 on the right-hand side of the equation

`3(y=-8/3x+15)\\3y=-8x+45\\8x+3y=45`