Answer:
Problem 2) : the gradient is "-2", and the y-intercept is "3"
Problem 3)
A is [tex]y=2x+2[/tex]
B is [tex]y=x+2[/tex]
Step-by-step explanation:
Problem 2)
In the line given by the equation: [tex]y=-2x+3[/tex]
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
[tex]y=-2x+3\\y=-2\,(0)+3\\y=3[/tex]
Problem 3)
Consider the two lines :
[tex]y=x+2[/tex] and [tex]y=2x+2[/tex]
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 [tex]y=x+2[/tex] ) that is the coefficient that multiplies the variable "x". While for the other line ( [tex]y=2x+2[/tex]) 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 [tex]y=2x+2[/tex], and the line identified with "B" is the one with smaller gradient [tex]y=x+2[/tex] .
