Question

In order to graph a line your equation must be set equal to y. If I gave you the following equation would you be able to graph it in the form it is given? If not, rewrite the equation so that you could graph it. - 6x + 12y = 9​

Answer 1

Answer:

Step-by-step explanation:

Graphing the equation in the form it is given is eventually hard so we always rewrite the equation in the form of y. Lets rewrite the equation in the form of y.

$-6x+12y=9\\12y=6x+9\\\\y=\frac{6x+9}{12} \\\\y=\frac{6x}{12}+\frac{9}{12} \\\\y=\frac{1}{2}x+\frac{3}{4}$

now if we compare it to our slope-intercept form which is

$y=mx+b$

m is the slope which is 1/2 which tells us that if the slope is positive the graph is a positive slope means that two variables are positively related that is, when x increases so does y, and when x decreases y also decreases. Graphically, a positive slope means that as a line on the line graph moves from left to right, the line rises, and b is the y-intercept which is 3/4.

Intercept means where the line intersects the specific axis. In this case b is y-intercept which is 3/4 which means the line intersects the y-axis at 3/4

so we have our first point (0 , 3/4)

now in order to graph the line we need one more point that is the x-intercept which means where the line would intersect the x-axis the coordinate would be (x , 0) so lets insert this coordinate into our equation that we rewrote above.

$y=\frac{1}{2}x+\frac{3}{4} \\\\0=\frac{1}{2}x+ \frac{3}{4}\\\\-\frac{3}{4}=\frac{1}{2} x\\\\-6=4x\\\\\frac{-6}{4}=x \\\\x=\frac{-3}{2}$

so our x-intercept is (-3/2 , 0)

Below I have attached the graph file you check it out for better understanding