Question

Which is an equation of the line through (0,0) and (2,-3)?

Answer 1

y = (-3/2)x

Explanation:

I am going to answer this question in slope-intercept form, which is y = mx + b (m is the slope, b is the y-intercept). The question already gives us the y-intercept, or the point at which the graph crosses the y-axis. It is (0, 0). Now, all we have to do is find the slope, which we can do using the following formula:

`m=(y_(2)-y_(1) )/(x_(2)-x_(1))`

In this formula, (x1, y1) and (x2, y2) are two points that are given to us [the first point is (0,0) and the second point is (2,-3). We can solve for the slope by plugging in:

`m=(-3-0)/(2-0)=(-3)/(2)`

Now that we have m and b, we can plug into slope-intercept form to get our equation: y = (-3/2)x + 0 or y = (-3/2)x

Answer 2

y = -1.5x

How to build equation?

Given points: (0, 0), (2, -3)

Find slope:

`\sf slope: (y_2 - y_1)/(x_2- x_1) \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points`

`\rightarrow \sf slope \ (m) = (-3-0)/(2-0) = -1.5`

Then find equation:

`y-y_1 = m(x - x_1)`

`y - 0 = -1.5(x -0)`

`y = -1.5x`