Write y − 2 = 3/2(x+2) in slope-intercept form.(1 point)

Question

Responses

y = 3/2x + 3/2
y equals Start Fraction 3 over 2 End Fraction x plus Start Fraction 3 over 2 End Fraction

y = 3/2 + 5x
y equals Start Fraction 3 over 2 End Fraction plus 5 x

y = 3/2x + 6
y equals Start Fraction 3 over 2 End Fraction x plus 6

y = 3/2x +5
y equals Start Fraction 3 over 2 End Fraction x plus 5

Answer 1

To write the equation y − 2 = 3/2(x+2) in slope-intercept form, we need to solve for y. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.

Let's solve the equation:

y − 2 = 3/2(x + 2)

First, distribute the 3/2 through the parenthesis:

y − 2 = 3/2 * x + 3/2 * 2

Now, multiply the 3/2 by 2:

y − 2 = 3/2x + 3

Next, add 2 to both sides to isolate y:

y = 3/2x + 3 + 2

Combine like terms:

y = 3/2x + 5

So, in slope-intercept form, the equation is:

y = 3/2x + 5

And if we were to write it using the "Start Fraction ... End Fraction" format, it would be:

y equals Start Fraction 3 over 2 End Fraction x plus 5