Consider the line y=9x-5.
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The two intersection points are (-2.79, -0.58) and (0.79, 6.58).
<h3>How to find the points of intersection?</h3>
Here we want to solve the system of equations:
y = 2x + 5
x² + y² = 36
To solve this, we need to replace the first equation into the second one:
x² + (2x + 5)² = 36
Now we can solve this for x:
x² + 4x² + 10x + 25 = 36
5x² + 10x - 11 = 0
This is a quadratic equation, to solve it we use the general formula:
So we have two solutions for x:
x = (-10 - 17.9)/10 = -2.79
x = (-10 + 17.9)/10 = 0.79
To get the y-values of the solutions, we evaluate the linear equation in these values of x:
y = 2*(-2.79) + 5 = -0.58
y = 2*( 0.79) + 5 = 6.58
Then the two intersection points are (-2.79, -0.58) and (0.79, 6.58).
If you want to learn more about intersection points:
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Slope intercept form: y = mx + b
mx = slope
b = y-intercept
We know the y intercept is 0, so nothing will be written there.
To find the slope of this line, we can use the slope formula.
We'll use the points (1, 0) and (3, 1) to find the slope.
Now we can just plug these values into the equation to find the slope.
1 - 0 / 3 - 1
1 / 2
The slope of the line is 1/2, or 0.5.
The slope-intercept form of this line can be written as:
y = 0.5x