Find the equation (in terms of x) of the line through the points (-1,4) and (4,-6) PLEASE HELP ME ANYONE

From the other question, remember that the general equation for slope-intercept form is y = mx + b, where m = the slope of the equation, b = the y intercept, and x and y are your variables (and the coordinate points on the graph). 

This time, we aren't given the value of m, the slope, so we have to find it ourselves. To find slope, use the equation:
[tex]slope = m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} [/tex]
where [tex]x_{2} [/tex] and [tex]y_{2} [/tex] are the x and y values of one coordinate point [tex](x_{2}, y_{2})[/tex], and [tex]x_{1}[/tex] and [tex]y_{1}[/tex] are the x and y values of another coordinate point [tex](x_{1}, y_{1})[/tex]. Since we are given two coordinate points, that means we can find the slope using that equation.

Let's choose (4, -6) as our [tex](x_{2}, y_{2})[/tex] coordinate points and (-1, 4) as our [tex](x_{1}, y_{1})[/tex] coordinate point, but you can switch them around, it doesn't matter! That means [tex]x_{2} = 4[/tex], [tex]y_{2} = -6[/tex], [tex]x_{1} = -1 [/tex], and [tex]y_{1} = 4[/tex]. Plug those values into your slope equation to find m:
[tex]slope = m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{-6 - 4}{4 - (-1)} = \frac{-10}{5} = -2[/tex]

That means your slope, m = -2. Now let's go back to our slope-intercept equation y = mx + b and plug m in. Now we have y = -2x + b. Like we did in that last problem, let's find b by plugging in one of our coordinate points! I'll plug in (-1, 4), but you can use (4, -6):
[tex]y = -2x + b\\ 4 = -2(-1) + b\\ 4 = 2 + b\\ b = 2 [/tex]

That means b = 2, so plug that into y = -2x + b to get your final equation:
Your answer is y = -2x + 2.