Question

Graph the line with a slope of 1 passing through the point (1,-5).

Answer 1

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

Where:

m: Is the slope

b: Is the cut-off point with the y axis

According to the data of the statement we have to:

$m = 1$

Then, the equation is of the form:

$y = x + b$

We substitute the point $(1, -5)$ and find "b":

$-5 = 1 + b\\-5-1 =b\\-6 = b$

Thus, the equation is of the form:

$y = x-6$

To graph we substitute the points on the coordinate axis:

$(x, y) :( 0, -6)$

For $x = 2$:$y = 2-6 = -4$ $(2, -4)$

For $x = 10$: $y = 10-6 = 4$ $(10,4)$

Answer:

$y = x-6$

See attached image