Question

Y = mx + c

explain what is this?
and how can we derive it practically??

Answer 1

Answer: First of all, refer to the attached photo to understand better.

Let us consider a straight line passing with intercept as "c" and slope as "m".

Again consider any variable point , let it be (x,y).

The intercept point be (0,c)

So slope can be found as ∆y/∆x

Therefore,

m = ∆y/∆x

=> m = (y-c)/(x-0)

=> m = (y-c)/x

=> mx = y-c

=> y = mx +c.

This the best way to prove the equation of a straight line

Explanation:

Answer 2

$\large{\underline{\underline{Correct\;Question:-}}}$

★ Derive the expression for y = mx + c.

$\large{\underline{\underline{Answer:-}}}$

y = mx + c

$\large{\underline{\underline{Explanation:-}}}$

$3x - 2y = 2 \\ </p><p>-2y = 2 - 3x \\ y = \frac{2}{ - 2} - \frac{3x}{ - 2} \\ y = - 1 - \frac{ - 3}{2}x \\ y = - 1 + \frac{3}{2}x \\ y = \frac{3}{2} x - 1$

Taking [x = 0]

$y = \frac{3}{2} \times 0 - 1 \\ y = - 1$

Taking [x = 2]

$y = \frac{3}{2} \times 2 - 1 \\ y =2$

Taking [x = 4]

$y = \frac{3}{2} \times 4 - 1 \\ y = 5$

★Therefore the points are :-

x = | 0 | 2 | 4 |

y = | -1 | 2 | 5 |

(x, y) = (0,-1) (2,2) (4,5)

★To Calculate the slope of a straight line :-

3x - 2y = 2

y = 1- 3x/2

y= (3x/2) - 1 ————> (y = mx + c)

$\large{\boxed{\tt{y = mx + c}}}$

Here, m is the slope. From the above equation we can make out that 3/2 represents the slope of the equation.

Note:- kindly refer the attachment for the graph.

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