Question

A line passes through the point (-2,7) and. Has a slope of -4. What is the value of a if the point (a, -2) is also on the line?

Answer 1

a = $\frac{1}{4}$

using the ' gradient formula '  m = (y₂ - y₁)/(x₂ - x₁) → (m is the slope)

here (x₁, y₁) = (a , - 2)) and (x₂ , y₂) = (- 2, 7)

thus $\frac{(7 + 2)}{(-2 - a)}$ = -4 ⇒$\frac{9}{(- 2 - a)}$ = -4

cross-multiply

-4(- 2 - a) = 9

8 + 4a = 9

subtract 8 from both sides

4a = 9 - 8 = $\frac{1}{4}$1

divide both sides by 4

a = $\frac{1}{4}$

Answer 2

you have to write a point slope equation which is formula: y-y1= slope(x-x1)

substitution this equation into your problem

y-7= -4(x-(-2)) ----------> y-7 = -4(x+2)

simplifying this equation

the equation is y=-4x -1

then you stated that (a,-2) then substitution this

-2 = -4x -1

-3 = -4x

x= 3/4

therefore a= 3/4