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

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 . To do that we are going to use the slope formula: .
From our two points we can infer that , , , . Lets replace those values in the slope formula:





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




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

Ithink it is 52