if a line has a slope of 2 and passes through (4,-1) what is the y-intercept?

Question

so confused please help :/

Answer 1

 

y - y₁ = m ( x - x₁ )   where m is the slope and (x₁,y₁) a point on the line.

 

                                the y-intercept is a special point on the line with x_intercept= 0 leading to y_intercept

 

m = 2

(x₁,y₁) = (4,-1)

 

y - (-1) = 2 ( x - 4 ) ---->  y + 1 = 2x - 8 ---->  y = 2x - 8 - 1

 

y = 2x - 9

 

y_intercept = 2 ( 0 ) - 9 = -9   Therefore the y-intercept is ( 0 , -9 )

 

Amanda, you'll be far less confused by mastering the concepts of slope, point, coordinates and intercepts. Math boils down to acquiring a whole new set of VOCABULARY! The rest is applying the concepts properly and logically !

Answer 2

Hi Amanda,

 

OK lets start with the slope intercept form of the equation of a line

 

It is

 

y = mx +b    (m is the slope and b is the y-intercept

 

OK  we know the slope is 2

 

so

 

y = 2x + b

 

now we also know the value of a point (4,-1) 

 

We can use that point in the equation to find b

 

-1 = 2(4)  + b

 

-1 = 8 + b

 

b = -9     (so the y intercept equals b and it equals -9

 

the final equation of the line

 

is

 

y = 2x - 9

 

Hope this helps