Any line with a slope different than 3 will intercept the given line only once.
<h3>What equation defines a line that intersects the graph?</h3>
The answer will be any line that is not parallel (nor the same) to the given line.
Remember two lines are parallel if the lines have the same slope and different y-intercept
In this case, the given linear equation is:
6x - 2y = 10
y = 3x - 5
So the slope is 3 and the y-intercept is -5.
Then, any line with a slope different than 3 will intercept this line only once.
An example can be:
y = 314*x
If you want to learn more about linear equations:
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The answer is 3/-2 hope that helps!
This equation can be solved graphically by plotting the equations
f(x) = 3^x
and
g(x) = 5x-1.
The x-coordinate of the point(s) of intersection is the solution.
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On my graphing calculator, I find it easier to locate x-intercepts, so I would rewrite the equation as
3^x -(5x -1) = 0
and plot the function
h(x) = 3^x -(5x -1)
The x-intercept(s) would be the solutions. (There are two: x≈0.577, x=2.)
Here's the answer with work hopefully it's good enough