Question

Sarita says the question of a line with a y-intercept of 7 that includes the point (3,-2) is y= -2/3x+7.Is she right if so explain why.If not,find the correct equation

Answer 1

The given equation y= -2/3 x+7 is NOT THE CORRECT equation.

y = -3 x + 7 is the correct equation.

Explanation:

Here, the given point on the equation is ( 3, -2)

Y - Intercept = 7

Now, the SLOPE INTERCEPT form of the given equation is

y = m x + C ; here, C = Y - Intercept, and m = Slope

Putting in the given values of C = 7 , (x,y) = (3,-2) find the slope.

⇒ -2 = m (3) + 7

or, -9 = 3m

⇒ m = -9/3 = -3

So, the slope of the equation is -3

SO, th equation of the line is given as

y = (-3) x + 7

or, y = -3x + 7 is the given line equation.

Hence, the given equation y= -2/3x+7 is NOT THE CORRECT equation.

Answer 2

She is not right.

Explanation:

Sarita says the equation of a line with a y-intercept of 7 that includes the point (3,-2) is
`y = - (2)/(3) x + 7` ........... (1)

She is not right.

Because, the equation of the straight line is in the slope-intercept form where 7 is the y-intercept but she said that the straight line includes the point (3,-2) which is not right as the point does not satisfy the equation.

Putting x = 3 in the equation (1) we get,y = - 2 + 7 = 5 ≠ -2

Therefore, the point (3,-2) is not on the line (1). (Answer)