find an equation of the line that passes through (2,-4) and is parallel to the line 3x-y=1. Write your answer in the form y=mx+b. please help!
First, find for m (slope):
3x-y=1
-y= 1-3x
y=3x-1 , therefore m= 3
If lines in parallel to 3x-y=1, then the slopes are the same. So, plug in to equation .
Y-Y2= m(X-X2)
y-(-4)=3(x-2)
y+4=3x-6
y=3x-10
To find the equation of a line parallel to another line, we need to determine the slope of the given line. The slope-intercept form of a line is y = mx + b, where m represents the slope of the line.
First, let's rearrange the equation of the given line, 3x - y = 1, into slope-intercept form:
y = 3x - 1
From this, we can see that the slope of the given line is 3. Since we want to find a line parallel to this, the parallel line will also have a slope of 3.
Now that we have the slope of the line we're looking for, we can use the point-slope form of a linear equation to find the equation of the line passing through (2, -4) with a slope of 3:
y - y1 = m(x - x1)
Plugging in the values, we get:
y - (-4) = 3(x - 2)
y + 4 = 3(x - 2)
y + 4 = 3x - 6
To write the equation in slope-intercept form (y = mx + b), we can simplify:
y = 3x - 6 - 4
y = 3x - 10
Therefore, the equation of the line passing through the point (2, -4) and parallel to the line 3x - y = 1 is y = 3x - 10.