Question

How to put the equation (10,-6) (5,1) in standard form

Answer 1

7x + 5y = 40 is the equation of line in standard form for (10, -6) and (5, 1)

Solution:

Given points are (10, -6) and (5, 1)

Let us first find the equation of line in slope intercept form and convert to standard form

The equation of line in slope intercept form is:

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

Where, "m" is the slope of line and "c" is the y intercept

The slope of line is given by formula:

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

Here points are (10, -6) and (5, 1)

$(x_1, y_1) = (10, -6)\\\\(x_2,y_2) = (5, 1)$

Substituting the values in slope formula,

$m = \frac{1-(-6)}{5-10}\\\\m = \frac{-7}{5}$

Find the y intercept

$\text{Substitute } m = \frac{-7}{5} \text{ and } (x, y) = (5, 1) \text{ in eqn 1}\\\\1 = \frac{-7}{5} \times 5 +c\\\\1 = -7+c\\\\c =8$

The equation of line is:

$\text{Substitute } m = \frac{-7}{5} \text{ and } c = 8 \text{ in eqn 1}\\\\y = \frac{-7}{5}x + 8$

Convert to standard form:

The standard form of an equation is Ax + By = C

In this kind of equation, x and y are variables and A, B, and C are integers

$y = \frac{-7}{5}x + 8\\\\y = \frac{-7x + 40}{5}\\\\5y = -7x + 40\\\\7x +5y = 40$

Thus equation of line in standard form is found