Find an equation of the line (in standard form) that is parallel to 2x+y=7 and passes through (-4,2)
To find an equation of the line parallel to 2x+y=7, we need to determine its slope. The given equation is already in slope-intercept form (y = mx + b), where m is the slope.
To get the slope, let's rearrange the equation 2x + y = 7 by isolating y:
y = -2x + 7
From this equation, we can see that the slope (m) is -2.
Since the line we're trying to find is parallel to this line, it will have the same slope of -2.
Now we can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
Plugging in the values of the point (-4, 2) and the slope (-2):
y - 2 = -2(x - (-4))
y - 2 = -2(x + 4)
y - 2 = -2x - 8
Rearranging this equation into standard form (Ax + By = C), where A, B, and C are integers:
2x + y = -2 - 8
2x + y = -10
So, the equation of the line parallel to 2x+y=7 and passing through (-4,2) in standard form is 2x + y = -10.