Question

PLLSS HELP THANK YOU:) What is the equation of the line in standard form? A function graph of a line with two points (-3,2) and (2,-1) with an x axis of negative five to five and a y axis of negative five to five
A.) x + 3y = 5
B.0 3x + 5y = 1
C.) 5x + 3y = 1
D.) x + 5y = 3?

Answer 1

Answer:

B. 3x + 5y = 1

Step-by-step explanation:

Since, the equation of a line passing through $(x_1, y_1)$ and $(x_2, y_2)$ is,

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

Thus, the equation of the line passes through the points (-3,2) and (2,-1) is,

$y - 2 =\frac{-1-2}{2+3}(x+3)$

$y-2 =-\frac{3}{5}(x+3)$

$5(y - 2) =-3(x +3 )$

$5y - 10 = -3x - 9$

$3x + 5y = -9 + 10$

$3x + 5y = 1$

∵ Standard form of a line is ax + by = c, where, a, b and c are any constants,

Hence, the required equation is,

3x + 5y = 1

i.e. OPTION B is correct.

Answer 2

A function graph of a line with two points (-3,2) and (2,-1)

Now we have to find the equation of line passing thorough these points

So let's find slope first using formula:

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{2-\left(-1\right)}{-3-2}=\frac{2+1}{-5}=-\frac{3}{5}$

Now plug the value of slope m and any point say (2,-1) into point slope formula:

$y-y_1=m\left(x-x_1\right)$

$y-\left(-1\right)=-\frac{3}{5}\left(x-2\right)$

Now we simplify it to get equation of the standard form Ax+By=C

$y+1=-\frac{3}{5}\left(x-2\right)$

$5\left(y+1\right)=-3\left(x-2\right)$

$5y+5=-3x+6$

$3x+5y+5=+6$

3x+5y=+6-5

3x+5y=1

Hence final answer is 3x+5y=1.