Write the equation in slope-intercept form of the line that is parallel to the given line and passes through the given point.
Y=2x+1; (5,-1)
Well... you know the form is y=mx +b where m is the slope.
So take the slope from Y=2x+1...which is the 2 so
You obtain Y=2x +b
now sub in (5, -1) which go in for the (x,y) the x and y in the equation y=2x+b, and solve for b :)
We would be happy to check your final answer :)
y=2x+b
-1=2(5)+b
I always get stuck around this part, have I been doing everything alright up to this point, and what steps do I need in order to solve it
-1=2(5)+b yes, correect
now
-1 = 10 + b
b = -11
so
y = 2 x - 11
To find the equation in slope-intercept form of a line that is parallel to the given line and passes through the given point, we need to use two pieces of information:
1. The slope of the given line.
2. The given point.
Given that the equation of the given line is y = 2x + 1, we can see that the slope of this line is 2.
To find the equation of a line parallel to the given line, it must have the same slope. Therefore, the slope of the line we want to find is also 2.
Now, using the point (5, -1), we can substitute the values into the slope-intercept form equation, y = mx + b, where m is the slope and b is the y-intercept.
So, let's substitute the values into the equation:
-1 = 2(5) + b
Simplifying the equation:
-1 = 10 + b
To solve for b, we can subtract 10 from both sides of the equation:
-1 - 10 = b
-11 = b
Now that we have the value of b, we can substitute it back into the slope-intercept form equation to get the final equation:
y = 2x - 11
Therefore, the equation in slope-intercept form of the line that is parallel to the given line y = 2x + 1 and passes through the point (5, -1) is y = 2x - 11.