The standard form equation for a line passing through the point (-3, 4) and parallel to the line denoted by y = 1/2x+4 is 2y - x = 11.
The standard form equation
ax + by = c
Here a, b, and c are constants and therefore use the slope-intercept form.
y = mx + c ...... (1)
where m is the slope, b = y-intercept
y = 1/2x + 4
Slope (m) = 1/2
It passes through a line that has points (-3,4)
Let's find c by putting the value of x = -3 and y = 4 in equation (1).
4 = 1/2 (-3) + c
4 = -3/2 + c
c = 4 + 3/2
=> c = (8+3)/2
=> c = 11/2
Therefore,
y = 1/2x + 11/2
y = (x+11)/2
=> 2y - x = 11
2y - x = 11 is the standard form of the line that passes through (-3,4) and is parallel to the line represented by y = 1/2x+4.
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