Question

Find the slope of the line joining the points (-1,5) and (6,-2). Also find the equation of that straight line. Find the intercepts on the x- and y axis

Answer 1

The slope of the line joining the points (-1,5) and (6,-2) is -1

x + y = 4 is the equation of line

x intercept is (-4, 0)

y intercept is (0, 4)

Solution:

Given that,

Points are (-1,5) and (6,-2)

The slope of line is given as:

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

From given,

$(x_1, y_1) = (-1, 5)\\\\(x_2, y_2) = (6, -2)$

Substituting the values we get,

$m = \frac{-2-5}{6+1}\\\\m = \frac{-7}{7}\\\\m = -1$

Thus slope of line is -1

The equation of line in slope intercept form is given as:

y = mx + c -------- eqn 1

Where,

m is the slope

c is the y intercept

Substitute m = -1 and (x, y) = (-1, 5) in eqn 1

5 = -1(-1) + c

5 = 1 + c

c = 4

Substitute m = -1 and c = 4 in eqn 1

y = -x + 4

In standard form,

x + y = 4 is the equation of line

Find x intercept:

Substitute y = 0

x + 0 = 4

x = -4

Thus x intercept is (-4, 0)

Find y intercept:

Substitute x = 0

0 + y = 4

y = 4

Thus y intercept is (0, 4)