write an equation in slope-intercept form for the line that is parallel to the given line and that passes through the given point.

y=1/2x+5:(4,-3)

If it is parallel, then it must have the form

y = (1/2)x + b , with (4, -3) on it
-3 = (1/2)(4) + b
-3 = 2 + b
b = -5

y = (1/2)x - 5

To write an equation in slope-intercept form for a line parallel to the given line and passing through the given point, we need to use the fact that parallel lines have the same slope.

The given line has the equation y = (1/2)x + 5. Since the slope of this line is 1/2, any line parallel to it will also have a slope of 1/2.

We also have the given point (4, -3) through which the line should pass. Let's call the equation of the line we want to find y = mx + b, where m represents the slope, and b represents the y-intercept.

Now, we know that the slope of the line we want is 1/2, so we can substitute m = 1/2 into the slope-intercept equation:

y = (1/2)x + b

We still need to find the value of b. To do this, we can substitute the x and y coordinates of the given point (4, -3) into the equation:

-3 = (1/2)(4) + b

Simplifying the right side:

-3 = 2 + b

Now, isolate b by subtracting 2 from both sides:

-3 - 2 = b

-5 = b

So the value of b is -5. Now we have the full equation:

y = (1/2)x - 5

Therefore, the equation in slope-intercept form for the line that is parallel to y = (1/2)x + 5 and passes through the point (4, -3) is y = (1/2)x - 5.