slope = [tex]\frac{4}{3}[/tex] and equation of line is
y = [tex]\frac{3}{2}[/tex] x + 3
calculate the slope m using the gradient formula
m = ( y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = 2, 7 ) and (x₂, y₂ ) = (- 1, 3 )
m = [tex]\frac{3-7}{-1-2}[/tex] = [tex]\frac{-4}{-3}[/tex] = [tex]\frac{4}{3}[/tex]
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
calculate m using the gradient formula
with (x₁, y₁ ) = (- 4, - 3) and (x₂, y₂ ) = (0, 3 )
m = [tex]\frac{3+3}{0+4}[/tex] = [tex]\frac{6}{4}[/tex] = [tex]\frac{3}{2}[/tex]
the line crosses the y-axis at (0, 3 ) hence c = 3
y = [tex]\frac{3}{2}[/tex] x + 3 ← equation of line
