Which of the following equations represents a line parallel to line ℓ

Solution:

We see that the slope of line ℓ is (0 - 3) / (2 - 0) = -3/2 and the y-intercept is 3. Therefore, the slope-intercept form of the line is y = (-3/2)x + 3. Instead of converting the equations (which are in general form) in the given choices to slope-intercept form, let’s convert the slope-intercept form to general form:

y = (-3/2)x + 3

2y = -3x + 6

3x + 2y = 6

Now, we use the fact that if two lines expressed in general form, Ax + By = C and Dx + Ey = F, are parallel, then A = D and B = E (and C ≠ F). That is, if two lines expressed in general form are parallel, they have identical coefficients of x and y. We see that 2y + 3x = 0 → 3x + 2y = 0 have the same coefficients of x and y as 3x + 2y = 6, thus it’s parallel to 3x + 2y = 6.

Answer: B

Straightforward actually.

Just follow the rule y = mx + c

Whatever is attached to x in numerical form is the slope.

From diagram we know that 0,3 and 2,0 are points on the line. Slope is y2-y1/x2-x1 = -3/2

Option B once simplified gives that answer.