Question

write an equation that is paraell to this equation

y-3=8/3(x+2); (-2,3)

Answer 1

To find an equation that is parallel to the given equation, we need to have the same slope.

The given equation is in slope-intercept form (y = mx + b) where the slope (m) is equal to 8/3.

So, any equation with a slope of 8/3 will be parallel to the given equation.

Let's use point-slope form to write the equation:

y - y1 = m(x - x1)

Since we want the equation to be parallel to the given equation and pass through the point (-2,3), we can substitute the point coordinates into the equation:

y - 3 = (8/3)(x - (-2))

Now, simplify:

y - 3 = (8/3)(x + 2)

Multiply both sides of the equation by 3 to eliminate the fraction:

3y - 9 = 8(x + 2)

Distribute 8:

3y - 9 = 8x + 16

To put the equation in standard form, move all the terms to one side:

8x - 3y = -25

Therefore, the equation that is parallel to the given equation (y - 3 = 8/3(x + 2)) and passes through the point (-2,3) is 8x - 3y = -25.