How do you write the point slope form of the equation given (-3,-3) parallel to #y=7/3x+3#?

Question

Avery Alexander · Accepted Answer

The equation is #y = 7/3x + 4#.

Parallel slopes mean equal slopes. Hence, by point-slope form: #y - y_1= m(x - x_1)# #y - (-3) = 7/3(x - (-3))# #y + 3 = 7/3x + 7# #y = 7/3x + 4# Hopefully this helps!

Kennedy Adams · Answer

undefined The point-slope form of the equation of a line is $ y - y_1 = m(x - x_1) $, where $ (x_1, y_1) $ is a point on the line and $ m $ is the slope of the line. Since the line is parallel to $ y = \frac{7}{3}x + 3 $, it has the same slope. So, the slope of the line is $ m = \frac{7}{3} $. Using the given point $ (-3, -3) $, we can substitute $ x_1 = -3 $ and $ y_1 = -3 $ into the point-slope form equation:

$$ y - (-3) = \frac{7}{3}(x - (-3)) $$

Simplify:

$$ y + 3 = \frac{7}{3}(x + 3) $$

Multiply both sides by 3 to clear the fraction:

$$ 3(y + 3) = 7(x + 3) $$

Distribute:

$$ 3y + 9 = 7x + 21 $$

Subtract 9 from both sides:

$$ 3y = 7x + 12 $$

Finally, divide both sides by 3 to solve for $ y $:

$$ y = \frac{7}{3}x + 4 $$

So, the point-slope form of the equation of the line parallel to $ y = \frac{7}{3}x + 3 $ and passing through $ (-3, -3) $ is $ y = \frac{7}{3}x + 4 $.