Question

Why an equation in slope-intercept form for the line that passes through (5, 4) and (6,-1)

Answer 1

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:

$m = \frac{y_2-y_1}{x_2-x_1}$

Here given points are (5, 4) and (6, -1)

$(x_1, y_1) = (5,4)\\\\(x_2,y_2) = (6, -1)$

Substituting the values in formula,

$m =\frac{-1-4}{6-5}\\\\m = \frac{-5}{1}\\\\m = -5$

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