Question

What is the equation of a line that has a slope of -2/3 and a x-intercept of -3?

Answer 1

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

$y = mx + b$

Where:

m: It's the slope

b: It is the cutting point with the y axis

We have, according to the statement data that:

$m = - \frac {2} {3}$

So, the equation is of the form:

$y = - \frac {2} {3} x + b$

We also have that the line intersects the "x" axis at -3, that is, the line passes through the point $(x, y): (- 3,0)$

We substitute to find "b":

$0 = -\frac {2} {3} (- 3) + b\\0 = -2 + b\\b = 2$

Finally, the equation is of the form:

$y = - \frac {2} {3} x + 2$

Answer:

$y = - \frac {2} {3} x + 2$