Answer :
Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slopw and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (3, 2) and (x₂, y₂ ) = (5, - 1)
m = [tex]\frac{-1-2}{5-3}[/tex] = - [tex]\frac{3}{2}[/tex], thus
y = - [tex]\frac{3}{2}[/tex] x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (3, 2), then
2 = - [tex]\frac{9}{2}[/tex] + c ⇒ c = 2 + [tex]\frac{9}{2}[/tex] = [tex]\frac{13}{2}[/tex]
y = - [tex]\frac{3}{2}[/tex] x + [tex]\frac{13}{2}[/tex] ← equation of line
Answer:
The equation of the line passing through the given points is
[tex]y=-\frac{3}{2}x+\frac{13}{2}[/tex]
Step-by-step explanation:
GIven two points are (3,2) and (5,-1)
To find the equation of the line passing through these two points
Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the two points (3,2) and (5,-1) respectively
Using the two points formula for finding slope:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m=\frac{-1-2}{5-3}[/tex]
[tex]m=\frac{-3}{2}[/tex]
Therefore [tex]m=-\frac{3}{2}[/tex]
By using formula:
[tex]y=mx+c[/tex]
Here Let (x,y) be (3,2)
[tex]y=mx+c[/tex]
[tex]2=-{\frac{3}{2}}\times 3+c[/tex]
[tex]2=\frac{-9}{2}+c[/tex]
[tex]c=\frac{9}{2}+2[/tex]
[tex]c=\frac{9+4}{2}[/tex]
[tex]c=\frac{13}{2}[/tex]
Therefore substitute values of m and c in
[tex]y=mx+c[/tex]
[tex]y=-\frac{3}{2}x+\frac{13}{2}[/tex]
Therefore the equation of the line passing through the given points is
[tex]y=-\frac{3}{2}x+\frac{13}{2}[/tex]