Question

What is the equation of the line that passes through point (6,18) and has a y-intercept of -2

Answer 1

y=\frac{10}{3} x-2

Explanation:

Notice that they are giving you two points on the plane that the line goes through:

1) the point (6,18), and

2) the point (0,-2) which is in fact the intersection of the line with the y axis.

So we use them to calculate first the slope of the line with the formula:

`slope= (y_2-y_1)/(x_2-x_1) \\slope=(18-(-2))/(6-0) \\slope=(20)/(6) =(10)/(3)`

Now that we know the slope, we can use it in the general "slope-intercept" form of a line and at the same time using the fact that we know the line's y-intercept (-2):

`y=mx+b\\y=(10)/(3) x+(-2)\\y=(10)/(3) x-2`