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.

facundo3141592 facundo3141592 · Answer 2 · 2021-08-12T20:03:58+02:00

A general linear equation can be written as:

y = a×x + b

Where a is the slope and b is the y-intercept.

In this case, we will found that the line is y = -2×x + 2

Now let's find the equation:

If we know that the line passes through the points (x₁, y₁) and (x₂, y₂), the slope can be written as:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

In this particular case, we know that the line passes through the points (-1,4) and (4,-6), then the slope of our line will be:

[tex]a = \frac{-6 - 4}{4 - (- 1)} = -10/5 = -2[/tex]

Then the line is something like:

y = -2×x + b

To find the value of b we can use one of the known points.

For example, if we use the point (-1, 4), this means that when x = -1 the value of y must be 4.

Replacing that in the equation we get:

4 = -2×-1 + b

4 = 2 + b

4 - 2 = b

2 = b

The equation of the line is y = -2×x + 2

The graph of this line can be seen in the image below:

If you want to learn more, you can read:

https://brainly.com/question/20542069