Answer
A) y - 5 = $\frac{7}{16}$(x + 3) or 7x - 16y = -101
B) y - 5 = $\frac{5}{3}$(x + 3) or 5x - 3y = -30
C) y - 5 = $\frac{4}{3}$(x + 3) or 4x -3y = -27
D) x = -3
Work Step by Step
For part A we know our slope is 7/16 and our point is (-3, 5). Therefore we can use point-slope form of y - y1 = m(x - x1) where m is the slope, to get y - 5 = 716(x + 3). If we want our answer in standard form we simply multiply to get rid of fractions and move everything to the left side so that it fits the formula of Ax + By = C to get 7x - 16y = -101. For part B we know it should be parallel to 5x - 3y = 3, which we can rearrange to the form of y = mx + b to find our slope of 5/3. Since we want our line to be parallel, it has the same slope and the point of (-3, 5), which we then plug into point-slope form to get y - 5 = 53(x + 3), or we can rearrange to standard form to get 5x - 3y = -30. For part C we know our line should be perpendicular to 3x +4y = 8, so again we rearrange this to y = mx + b to find a slope of -3/4, and since we want our line to be perpendicular to this, we must take the opposite reciprocal of this slope. Therefore our slope is 4/3 and our point is still (-3, 5) so in point slope-form our line is y - 5 = 43(x + 3), and in standard form it is 4x -3y = -27. Finally, for part D, we know that our line should be parallel to the y-axis. This means it’s slope is undefined and it is simply x = something. Because we are given (-3, 5), it is x = -3.
