Question

A line has a slope of 1/4 and passes through point (0.4,-1/2) . What is the value of the y-intercept?

A. –0.6
B. –0.4
C. 0.275
D. 0.525

Answer 1

Hello:

the equation is : y = ax+b when : a is the slope

a = 1/4 .. so : y = (1/4)x +b

passes through point (0.4,-1/2) : - 1/2 = (1/4)(0.4) + b

b = - 1/2 - 0.4/4 = (-2 -0.4)/ 4

b = - 2.4/4

y = (1/4)x - 2.4/4

the y-intercept if x= 0 y = -2.4/4 = - 0.6 ...( answer : A )

Answer 2

A. - 0.6

Explanation:

Since, the equation of a line passes through
`(x_1,y_1)`, having slope m is,

`y-y_1=m(x-x_1)`

Thus, the equation of the line passes through point (0.4,-1/2) and has the slope of 1/4 is,

`y-(-(1)/(2))=(1)/(4)(x-0.4)`

`\implies y+(1)/(2)=(1)/(4)(x-0.4)`

For y-intercept, x = 0,

`\implies y+(1)/(2)=(1)/(4)(-0.4)`

`\implies y + 0.5 = -0.1`

`\implies y = -0.1-0.5 = -0.6`

Hence, the value of the y-intercept is -0.6.

Option 'A' is correct.