Question

Parallel to y=2/3x+4 and goes through (-9,-2)

Answer 1

Hey there :)

y = $\frac{2}{3}x + 4$

Since this line is parallel to the line to be found, both have the same slope: $\frac{2}{3}$

Coordinates: ( - 9 , - 2 )

y - ( -2 ) = $\frac{2}{3}$ ( x - ( -9 ) )
$y + 2 = \frac{2}{3} x + 6$
$y = \frac{2}{3} x + 6 - 2$

$y = \frac{2}{3}x + 4$

Answer 2

Hi there! The answer is y = 2/3x + 4

When the line we are looking for is parallel to y = 2/3x + 4, the slope is the same as in the line mentioned before. Hence, we get the following formula:
$y = \frac{2}{3}x + b$

In this equation, b represents a number. Since the line passes through the point (-9, -2) we can plug in the coordinates into the formula. Then we get the following:
$\frac{2}{3} * -9 + b = -2$
$-6 + b = -2$

Now we add 6 to both sides of the equation
$b = 4$

We've now found our answer, the formula of the line, which is:
y = 2/3x + 4