Question

Can someone help me with these

Answer 1

Answer:

Problem 2) : the gradient is "-2", and the y-intercept is "3"

Problem 3)

A is  $y=2x+2$

B is $y=x+2$  

Step-by-step explanation:

Problem 2)

In the line given by the equation:   $y=-2x+3$

the "gradient" (also known as "slope") is the numerical coefficient that multiplies the variable "x". So in this case the gradient is "-2"

the y-intercept is the numerical term "+3" because that is the y-value result of evaluating the expression for x = 0

$y=-2x+3\\y=-2\,(0)+3\\y=3$

Problem 3)

Consider the two lines :

$y=x+2$  and  $y=2x+2$

notice that both have the same y-intercept (that is the numerical term "2" at the end of both expressions. That means that both lines cross the y-axis at the point y=2.

Now notice that the gradient of one of them is "1"  (for $y=x+2$ ) that is the coefficient that multiplies the variable "x". While for the other line ( $y=2x+2$)  the gradient is "2" and therefore steeper than the previous one.

Then, the line identified as "A" which is the one with steeper gradient, corresponds to the equation   $y=2x+2$, and the line identified with "B" is the one with smaller gradient  $y=x+2$  .