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:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{2-\left(-1\right)}{-3-2}=\frac{2+1}{-5}=-\frac{3}{5}[/tex]
Now plug the value of slope m and any point say (2,-1) into point slope formula:
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y-\left(-1\right)=-\frac{3}{5}\left(x-2\right)[/tex]
Now we simplify it to get equation of the standard form Ax+By=C
[tex]y+1=-\frac{3}{5}\left(x-2\right)[/tex]
[tex]5\left(y+1\right)=-3\left(x-2\right)[/tex]
[tex]5y+5=-3x+6[/tex]
[tex]3x+5y+5=+6[/tex]
3x+5y=+6-5
3x+5y=1
Hence final answer is 3x+5y=1.
Answer:
B. 3x + 5y = 1
Step-by-step explanation:
Since, the equation of a line passing through [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is,
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
Thus, the equation of the line passes through the points (-3,2) and (2,-1) is,
[tex]y - 2 =\frac{-1-2}{2+3}(x+3)[/tex]
[tex]y-2 =-\frac{3}{5}(x+3)[/tex]
[tex]5(y - 2) =-3(x +3 )[/tex]
[tex]5y - 10 = -3x - 9[/tex]
[tex]3x + 5y = -9 + 10[/tex]
[tex]3x + 5y = 1[/tex]
∵ 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.
