1)An equation in the slope-intercept form is written as
y=mx+by=mx+b
Where m is the slope of the line and b is the y-intercept. You can use this equation to write an equation if you know the slope and the y-intercept.
Example
Find the equation of the line
Choose two points that are on the line
Calculate the slope between the two points
<span><span>m=<span>y2−y1x2−x1</span>=<span><span>(−1)−3</span><span>3−(−3)</span></span>=−46=−23</span><span>m=<span>y2−y1x2−x1</span>=<span><span>(−1)−3</span><span>3−(−3)</span></span>=−46=−23</span></span>
We can find the b-value, the y-intercept, by looking at the graph
b = 1
We've got a value for m and a value for b. This gives us the linear function
<span>y=−23x+1y=−23x+1</span>
In many cases the value of b is not as easily read. In those cases, or if you're uncertain whether the line actually crosses the y-axis in this particular point you can calculate b by solving the equation for b and then substituting x and y with one of your two points.
We can use the example above to illustrate this. We've got the two points (-3, 3) and (3, -1). From these two points we calculated the slope
<span>m=−23m=−23</span>
This gives us the equation
<span>y=−23x+by=−23x+b</span>
From this we can solve the equation for b
<span>b=y+23xb=y+23x</span>
And if we put in the values from our first point (-3, 3) we get
<span><span>b=3+23⋅(−3)=3+(−2)=1</span><span>b=3+23⋅(−3)=3+(−2)=1</span></span>
If we put in this value for b in the equation we get
<span>y=−23x+1y=−23x+1</span>
which is the same equation as we got when we read the y-intercept from the graph.
To summarize how to write a linear equation using the slope-interception form you
Identify the slope, m. This can be done by calculating the slope between two known points of the line using the slope formula.Find the y-intercept. This can be done by substituting the slope and the coordinates of a point (x, y) on the line in the slope-intercept formula and then solve for b.
Once you've got both m and b you can just put them in the equation at their respective position.
https://www.mathplanet.com/education/algebra-1/formulating-linear-equations/writing-linear-equations.....
2)https://www.cymath.com/answer?q=6x%20%2B%202y%20%3E%204
3)https://www.cymath.com/answer?q=9x%20%E2%80%93%203y%20%3D%2012
