Question

please help thank youWhat is the point-slope form of the equation of the line through theses two points(-1,3) and (3,-4)

Answer 1

The slope (m) of the line that passes through two points (x1, y1) and (x2, y2) is computed as follows:

`m\text{ = }(y_2-y_1)/(x_2-x_1)`

Replacing with points (-1,3) and (3,-4)​:

`m\text{ = }(-4-3)/(3-(-1))=(-7)/(4)`

In point-slope form, the equation of a line is:

y = mx + b

where m is the slope and b the y-intercept

Now we have the slope, we can use it in combination with one of the given points to find b. Replacing with x = -1, y = 3 and m = -7/4, we get:

3 = -7/4*(-1) + b

3 = 7/4 + b

3 - 7/4 = b

5/4 = b

Then, the equation is:

y = -7/4x + 5/4