Question

Write an equation that is parallel to y = 1/2x + 2 and goes through the point (2,-3)

Answer 1

All you need to do is change the point st which the line crosses the y-axis. 1/2x + will work.

Answer 2

Slope-intercept form:  y = mx + b

(m is the slope, b is the y-intercept or the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis)

For lines to be parallel, they need to have the same slope.

$y=\frac{1}{2} x+2$    The slope is 2, so the parallel line's slope is also 2.

Now that you know the slope, substitute/plug it into the equation:

y = mx + b

$y=\frac{1}{2} x+b$    To find b, plug in the point (2, -3) into the equation, then isolate/get the variable "b" by itself

$-3=\frac{1}{2}(2)+b$

-3 = 1 + b    Subtract 1 on both sides to get "b" by itself

-3 - 1 = 1 - 1 + b

-4 = b

$y=\frac{1}{2} x-4$