Respuesta :
Given:
A.)
Slope of the line (m) = -2/3
Y-intercept (b) = 3
The given can be used to make an equation under the Slope-Intercept Form:
[tex]\text{ y = mx + b}[/tex]By substituting m and b to y = mx + b, we can generate the equation.
We get,
[tex]\text{ y = mx + b}[/tex][tex]\text{ y = (-2/3)x + (3)}[/tex][tex]\text{ y = -}\frac{2}{3}x\text{ + 3}[/tex][tex]3(\text{ y = -}\frac{2}{3}x\text{ + 3)}[/tex][tex]3y\text{ = -2x + 9}[/tex][tex]2x\text{ + 3y = 9}[/tex]Therefore, the equation match to m = -2/3 and b = 3 is 2x + 3y = 9.
B.)
Slope of the line (m) = -3/2
x,y = 4,-1
To be able to generate the equation, let's first determine the y-intercept (b). We can get it by substituting m = -3/2 and x,y = 4,-1 to the equation y = mx + b.
We get,
[tex]\text{ y = mx + b}[/tex][tex]\text{ -1= (-3/2)(4) + b}[/tex][tex]-1\text{ = }\frac{-12}{2}\text{ + b }\rightarrow\text{ -1 = -6 + b}[/tex][tex]\text{ b = -1 + 6}[/tex][tex]\text{ b = 5}[/tex]Since we now found that the y-intercept (b) = 5, let's substitute b and m = -3/2 to y = mx + b to generate the equation.
We get,
[tex]\text{ y = mx + b}[/tex][tex]\text{ y = (-3/2)x + (5)}[/tex][tex]\text{ y = -}\frac{3}{2}x\text{ + 5}[/tex][tex]\text{ -2(y = -}\frac{3}{2}x\text{ + 5)}[/tex][tex]\text{ -2y = 3x - 10}[/tex]Therefore, the equation that match m = -3/2 and (4,-1) is -2y = 3x - 10.
