Question

The graph of the equation y = mx + c passes through
the points (1, 4) and (-2,-5). Determine the values
of m and c.​

Answer 1

EXPLANATION.

Graph of the equation : y = mx + c.

Passes through the point (1,4) and (-2,-5).

As we know that,

Put the value of the point (1,4) in the equation, we get.

⇒ y = mx + c.

⇒ 4 = m(1) + c.

⇒ 4 = m + c. - - - - - (1).

Put the value of the point (-2,-5) in the equation, we get.

⇒ y = mx + c.

⇒ -5 = m(-2) + c.

⇒ -5 = -2m + c.

⇒ -5 + 2m = c.

⇒ 2m - 5 = c. - - - - - (2).

Put the value of equation (2) in equation (1), we get.

⇒ 4 = m + (2m - 5).

⇒ 4 = m + 2m - 5.

⇒ 4 + 5 = m + 2m.

⇒ 9 = 3m.

⇒ m = 3.

Put the value of m = 3 in the equation (2), we get.

⇒ c = 2m - 5.

⇒ c = 2(3) - 5.

⇒ c = 6 - 5.

⇒ c = 1.

Value of m = 3 and c = 1.

                                                                                                                       

MORE INFORMATION.

Different forms of equation of straight line.

(1) = Slope - Intercept form : y = mx + c.

(2) = Slope point form : The equation of a line with slope m and passing through a point (x₁, y₁) is (y - y₁) = m(x - x₁).

(3) = Two point form = (y - y₁) = (y₂ - y₁)/(x₂ - x₁) (x - x₁).

(4) = Intercept form : x/a + y/b = 1.

(5) = Normal (perpendicular) form of a line : x cosα + y sinα = p.

(6) = Parametric form(distance form) = (x - x₁)/cosθ = (y - y₁)/sinθ = r.

Answer 2

Given :-

The graph of the equation y = mx + c passes through

the points (1, 4) and (-2,-5).

To Find :-

Value of m and c

Solution :-

Putting x = 1

4 = m(1) + c

4 = m + c (1)

Now, In second equation

5 = m(-2) + c

5 = -2m + c

5 = 2m - c(2)

Now

Adding 1 and 2 will give -

5 + 4 = m + c + (2m - c)

9 = m + c + 2m - c

9 = 3m

9/3 = m

3 = m

Using 1

4 = m + c

4 = 3 + c

4 - 3 = c

1 = c