The slope (m) of the line that passes through two points (x1, y1) and (x2, y2) is computed as follows:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]
Replacing with points (-1,3) and (3,-4):
[tex]m\text{ = }\frac{-4-3}{3-(-1)}=\frac{-7}{4}[/tex]
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
