Answer:
C
Step-by-step explanation:
the equation of a line in slope-intercept form is
y = mx + c ( m is the slope and c the y-intercept )
to calculate m use the gradient formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ( = (2, 3) and (x₂, y₂ ) = (4, - 7)
m = [tex]\frac{-7-3}{4-2}[/tex] = [tex]\frac{-10}{2}[/tex] = - 5
y = - 5x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (2, 3 ), then
3 = - 10 + c ⇒ c = 3 + 10 = 13
y = - 5x + 13 ← equation in slope-intercept form (1)
Add 5x to both sides
5x + y = 13 ← equation in standard form (2)
We can also express the equation in point- slope form
y - b = m(x - a )
where (a, b ) is a point on the line → using (4, - 7), then
y + 7 = - 5(x - 4 ) ← equation in point- slope form (3)
