Write the equation of the line that passes through the given point and is parallel to the given line. IN SLOPE INTERCEPT FORM.

Question

Write the equation of the line that passes through the given point and is parallel to the given line. IN SLOPE INTERCEPT FORM.

Answer 1

Given

Y = (2/3)*x-2

Find

Parallel equation at points (3,-4)

Solution

In order for 2 equations to be parallel they need to have the same slope.

Therefore, the slope of the parallel equation is m = 2/3

Now to put this in slope intercept form

Y = mx + b

m = slope

b = y-intercept

Knowing the slope is m=2/3

The parallel equation is thus far

Y = (2/3)x+b

Apply the points of interest

-4 = (2/3)*(3) + b

-4 - 2 = b

b = -6

Solution

Y = (2/3) x - 6

Answer 2

The slope intercept form is y = mx + b where m = gradient, and b = y intercept

y = ²/₃ x - 2 is already in this form (if not, rearrange to make it so) m = 2/3 b = -2

parallel lines have same gradient (or m1 = m2).

hence, general equation for lines parallel to given line is y = ²/₃ x + n

for specific line passing through (3,-4) we want to substitute these values and solve for n:

hence, (-4) = ²/₃ (3) + n

=> -4 - 2 = n

=> n = -6

so our desired equation is y = ²/₃ x - 6