Question 272643: The problem is: 4x - y =7
I need to determine if it is a linear equation or not. i need to explain the problem and try to share at least 3 orderd pairs of points that would be solutions to this equation.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! a linear equation is an equation in which the highest order of exponent is 1.
your equation is:
4x - y = 7
it's a linear equation.
none of the variables has an exponent larger than 1.
x = x^1
y = y^1
to find your ordered pairs, just take 3 values for x at random and plug them into the equation.
let x = 1,2,3
your equation is:
4x - y = 7
if you solve for y, it makes it easier to find the y value given the x value.
solve for y to get:
y = 4x - 7
when x = 1, y = -3
when x = 2, y = 1
when x = 3, y = 5
placing the equation into this form also allows you to graph it.
placing the equation into this form also gives you the slope-intercept form of the equation.
what you started with was the standard form of the equation for a straight line.
that standard form is ax + by = c
your equation is:
4x - y = 7
a = 4 and b = -1
the slope intercept form of the equation of a straight line is y = mx + b
m is the slope and b is the y intercept.
when you solved for y, you placed the equation into this form.
your slope is 4
your y intercept is -7
graph of your equation looks like this:
I placed horizontal lines at y = -3, 1, 5.
If you trace a vertical line down from the intersections of those lines with the line created by your equation, you will see that the value of x at those intersection points is 1,2,3
the points on the line formed by your equation are:
(x1,y1) = (1,-3)
(x2,y2) = (2,1)
(x3,y3) = (3,5)
you can take any other values of x and find the corresponding value of y by just replacing x in the equation with the value of x.
the equation is y = 4x - 7
when x = 5, y = 20-7 = 13, etc.
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