Question

Write the equation, in slope-intercept form, of the line passing through the origin and the point $(-4,3)$.

Answer 1

If the equation is passing trough the origin, it will be passing trough the point (0,0). We now for our problem that the equations is also passing trough the point (-4,3). So, our line is passing trough the points (0,0) and (-4,3). To write the equation in slope-intercept form, first, we need to find its slope
`m`. To do that we are going to use the slope formula:
`m= (y_(2)-y_(1))/(x_(2)-x_(1))`.
From our two points we can infer that
`x_(1)=0`,
`y_(1)=0`,
`x_(2)=-4`,
`y_(2)=3`. Lets replace those values in the slope formula:

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

`m= (3-0)/(-4-0)`

`m= (3)/(-4)`

`m=- (3)/(4)`

Now that we have our slope, we can use the slope-intercept formula:

`y-y_(1)=m(x-x_(1))`

`y-0=- (3)/(4) (x-0)`

`y=- (3)/(4) x`

We can conclude that the equation of the line passing trough the points (0,0) and (-4,3) is
`y=- (3)/(4) x`.