Give the equation of the line that passes through point ( 1, -3) and is parallel to the line y = 2x - 8.

Since your new line is parallel to y = 2x + 8, it must differ only in the constant, so let it by

y = 2x + b
sub in the point (1,-3)
-3 = 2 + b
b = -5

new equation: y = 2x - 5

To find the equation of a line parallel to another line, we need to remember that parallel lines have the same slope. The given line has a slope of 2, which means the line we are looking for will also have a slope of 2.

The equation of a line can be represented in the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. We can use the given point (1, -3) to find the y-intercept.

Substituting the values of x and y from the given point into the equation, we get:

-3 = 2(1) + b

Simplifying, we have:

-3 = 2 + b

To isolate b, we subtract 2 from both sides:

-3 - 2 = b

-5 = b

Now we have the slope (m = 2) and the y-intercept (b = -5). We can plug these values into the equation y = mx + b to get the final equation:

y = 2x - 5

Therefore, the equation of the line that passes through the point (1, -3) and is parallel to the line y = 2x - 8 is y = 2x - 5.