y = -5x + 29 is the equation of line in slope intercept form for the line that passes through (5, 4) and (6,-1)
Solution:
Given that, line that passes through (5, 4) and (6,-1)
To find: Equation of line in slope intercept form
Let us first find the slope of line
The slope of line is given by formula:
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
Here given points are (5, 4) and (6, -1)
[tex](x_1, y_1) = (5,4)\\\\(x_2,y_2) = (6, -1)[/tex]
Substituting the values in formula,
[tex]m =\frac{-1-4}{6-5}\\\\m = \frac{-5}{1}\\\\m = -5[/tex]
The equation of line in slope intercept form is given as:
y = mx + c ------------ eqn 1
Where, "m" is the slope of line and "c" is the y - intercept
To find y - intercept, substitute m = -5 and (x, y) = (5, 4) in eqn 1
4 = -5(5) + c
4 = -25 + c
c = 29
Substitute m = -5 and c = 29 in eqn 1 to get equation of line
y = -5x + 29
Thus equation of line in slope intercept form is found