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

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:

From given,

Substituting the values we get,

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)

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3

question: how many people can she serve?

answer: she can serve 16.66666667 people. so she can only give 16 people a complete serving.

question: does she have enough ice cream for her guests?

answer: no. explanation: she only has enough for 16 people to have a full serving. however, she can give a 17th person a partial serving.