Write the equation of the line with x-intercept 3 and y-intercept 2.

a) y = 2 3 x + 2
b) y = 3 2 x + 2
c) y = − 2 3 x + 2
d) y = − 3 2 x + 2

y=−23x+2

explanation:

by definition the x-intercept of 3 is the point (3, 0) and

by definition the y-intercept of 2 is the point (0, 2).

because we have two points we can use the point-slope formula to determine the equation. in order to use the point-slope formula we must first determine the slope of the line.

the slope can be found by using the formula: m=y2=y1x2−x1

where m is the slope and (x1,y1) and (x2,y2) are the two points.

substituting the two points from the problem gives the slope as:

m=0−23−0

m=−23

now that we have the slope we can use the point-slope formula to determine the equation of the line:

the point-slope formula states: (y−y1)=m(x−x1)

where m is the slope and #(x_1, y_1) is a point the line passes through.

we can substitute the slope we calculated and one of the points to give:

y−0=−23(x−3)

y=−23x+23⋅3

y=−23x+2answer:

step-by-step explanation:

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

60°

step-by-step explanation:

the measure angle of c in an isosceles triangle abc is 60° because in isosceles triangle,the measures of all the angles is 60°.