Question

how do i find the equation for the lines:

1. y-intercept of -2.1, x-intercept of 3.5

2. through (1.2,5.1), x-intercept of 3.7

Answer 1

In factored form:
y=a(x-á)(x-â)
The alpha and beta symbols are the x-intercepts (or roots). If you plug in the x-inercept, and then the point that you know, you can find the value of 'a' and thus form an equation.

For your first one:
sub in the root
y=a(x-(3.5))
sub in the point
-2.1=a(0-3.5)
-2.1=a(-3.5)
a=0.6

Therefore: y=0.6(x-3.5)

Answer 2

I apologize, the alpha and beta symbols didn't show up. The a's with accents over them are the roots.

As well, I made a mistake in the final equation (forgot a letter).

y=0.6x(x-3.5)

Answer 3

1. y = 0 at the x-int.
x = 0 at the y -jnt.
(0 , -2.1), (3.5 , 0),

Slope = ((0 - (-2.1)) / (3.5 - 0) = 3/5
y = mx + b,
-2.1 = (3/5)*0 + b,
b = -2.1,

Eq: y = (3/5)x - 2.1.

2. (1.2 , 5.1) , (3.7 , 0),
Slope = (0 - 5.1) / (3.7 - 1.2) =
-5.1/2.5 = -2.04,

y = mx + b,
5.1 = -2.04*1.2 + b,
5.1 = -2.45 + b,
b = 5.1 + 2.45 = 7.55,

Eq: y = -2.04x + 7.55.

Answer 4

through (3.5, -2.3), x-intercept 5.1