Question

Choose the equation below that represents the line passing through the point (1, -4) with a slope of 1/2

Answer 1

For this case we have that by definition, the line equation of the slope-intersection form is given by:

$y = mx + b$

Where:

m: It's the slope

b: It is the cut-off point with the y axis

According to the statement we have:

$m = \frac {1} {2}$

Thus, the equation is of the form:

$y = \frac {1} {2} x + b$

We substitute the given point and find "b":

$-4 = \frac {1} {2} (1) + b\\-4 = \frac {1} {2} + b\\-4- \frac {1} {2} = b\\b = - \frac {9} {2}$

Finally, the equation is of the form:

$y = \frac {1} {2} x- \frac {9} {2}$

Answer:

$y = \frac {1} {2} x- \frac {9} {2}$