Write an equation of the line that passes through
(2, -1) and is parallel to the graph of y = 5x – 2.
Write your final equation in slope-intercept form.
Since the line we are looking for is parallel to the graph of y = 5x - 2, it will have the same slope.
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
We know that the slope of the line we want is 5, so our equation so far is y = 5x + b.
To find the value of b, we can use the coordinates of the point (2, -1) that the line passes through.
Substituting 2 for x and -1 for y in the equation, we get -1 = 5(2) + b.
Simplifying the equation, we have -1 = 10 + b.
To isolate b, we subtract 10 from both sides of the equation:
-1 - 10 = b
-11 = b
Now we have the values for both m (5) and b (-11), so our final equation is:
y = 5x - 11.