Question

What is an equation of the line that passes through the points (0, 3) and (5, -3)?

Answer 1

Answer (assuming it can be in slope-intercept form):

`y = -(6)/(5) x+3`

Explanation:

1) First, use the slope formula
`m =(y_2-y_1)/(x_2-x_1)` to find the slope of the line. Substitute the x and y values of the given points into the formula and solve:

`m =((-3)-(3))/((5)-(0)) \\m = (-3-3)/(5-0)\\m = (-6)/(5)`

So, the slope is
`-(6)/(5)`.

2) Now, use the slope-intercept formula
`y = mx + b` to write the equation of the line in slope-intercept form. All you need to do is substitute real values for the
`m` and
`b` in the formula.

Since
`m` represents the slope, substitute
`-(6)/(5)` for it. Since
`b` represents the y-intercept, substitute 3 for it. (Remember, the y-intercept is the point at which the line hits the y-axis. All points on the y-axis have an x-value of 0. Notice how the given point (0,3) has an x-value, too, so it must be the line's y-intercept.) This gives the following equation and answer:

`y = -(6)/(5) x+3`