Tell whether each equation has one, zero, or infinitely many solutions.5(x - 3) +6= 5x - 9
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Answer:
My blue dot is the y-intercept.
My red dot is my x-intercept.
Please look at the graph.
Step-by-step explanation:
I can show you my graph and mark it where the x-intercepts and y-intercepts are.
Let's begin.
We have y=2/3 x+4.
Compare this to the slope-intercept form, y=mx+b where m is the slope and b is the y-intercept.
You should see that m=2/3 and b=4.
This means the slope is 2/3 and the y-intercept is 4.
Don't forget slope means rise/run.
So once we graph 4 (plot a point) on the y-axis, then we will use our slope to get to one more point. The slope here tells us to rise 2 and run 3.
Now sometimes our graph is not accurate when drawing by hand so there is a way without graphing that you can find the x- and y-intercepts.
The x-intercept is when the y-coordinate is 0.
The y-intercept is when the x-coordinate is 0.
So to find the x-intercept, I'm going to set y to 0 and solve for x. Like so,
0=2/3 x +4
Subtract 4 on both sides:
-4=2/3 x
Multiply both sides by the reciprocal of 2/3 which is 3/2:
3/2 (-4)=x
Simplify:
-12/2=x
Simplify:
-6=x
Symmetric Property:
x=-6
So the x-intercept is (-6,0).
I actually already have the y-intercept since my equation is in y=mx+b (slope-intercept form). But if it wasn't you could just set x to 0 and solve for y. Like so:
y=2/3 (0)+4
y=0+4
y=4
The y-intercept is (0,4).
Let's go to our graph now.
