Question

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

Answer 1

Answer:

y = -1.5x

How to build equation?

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

Find slope:

$\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points$

$\rightarrow \sf slope \ (m) = \dfrac{-3-0}{2-0} = -1.5$

Then find equation:

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

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

$y = -1.5x$

Answer 2

Answer:

y = (-3/2)x

Step-by-step 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:

$m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}$

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:

$m=\frac{-3-0}{2-0}=\frac{-3}{2}$

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