Question 272643
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:


{{{graph(600,600,-1,4,-10,10,4x-7,-3,1,5)}}}


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.