 # In mathematics, a linear equation is an equation that involves only the variables (no exponents or roots) and the coefficients of the variables are all constants. Linear equations can be written in the form "ax" + "by" + "cz" = "d", where a, b, c and d are constants, and a, b, and c are not zero. The solutions of the linear equation are the values of "x", "y" and "z" that satisfy the equation.

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So in this example, we're going to graft the equation. Four X minus five y is equal to 20. Well, this equation is in standard form because it's in the form a X plus B y equals C, where a, B and C are just Constance. So remember when we graph equations in standard form, what we need to do first is find the X and y intercepts. So let's start by finding the X intercept. So remember, X intercept is the point on your graph that where crosses the X axis Well, any point that's on your X axis has to John Reform X comma zero. So it's why corn it is always zero, and the X value just depends on your equation. So to find your ex intercept, what we're going to dio is substitute zero in place of why in our equation, So when we do that, we'll have four X minus five times zero is equal to 20. And now we just have to solve this equation for X Well, negative five times zero is just zero. So this park cancels so we're left with four X is equal to 20. So the solve for X we're going to divide both sides of our equation by four and 20. Divided by four is five. That means our X intercept will take on the form 50 So let's go ahead and plot that point so we'll go to the right five and plot it. So this is one point on our graph. Well, now that we know the x intercept, we're gonna go ahead and find the Y intercept. I remember the Y intercept tells us the point on our line that it hits the oh, the Y axis. Now, for any point that falls on our Y axis is going to take on the general form zero comma y. So the X coordinate is always zero and the white corn, it varies from equation to equation. So the salt for our Y intercept, we're going to substitute zero and place of acts in our original equation. So we're gonna have four times zero minus five. Y is equal to 20 and then we just solve the equation for why? Well, four times zero is zero. So this park cancels, so we're just left with negative five y is equal to 20. So the salt for why we're gonna divide both sides of our equation by negative five and 20. Divided by negative five is negative. Four. So our why intercept is negative for so in terms of an ordered pair, the ordered pair would be zero negative four. And now that we know our y intercept, we can go ahead and plot it. So the plot this point, we simply go down. For now that we know two points on our line, we just now need to draw the line that connects T, connects them and make sure you go all the way through. Because, remember, a line goes on infinitely in both directions. So now we have graft the equation. Four x minus five y equals 20. Syracuse University
##### Top Algebra Educators  ##### Heather Z.

Oregon State University  ##### Michael J.

Idaho State University