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When it is a line through the origin.
Given a point P = (a,b) and slope m, the equation of a line through P with slope m is (y-b) = m(x-a)
The straight line equation is: y = 2x
You can have infinitely many lines through one specific point, each with a different equation. If you want to have a general equation for ANY line that goes through that point, use the point-slope equation for a line, and use a variable for the slope.
If the equation of a line is in the form ax + by + c = 0 then the slope of the line will be -a/b.
When it is a line through the origin.
Write the equation of a line in slope-intercept form that has a slope of -2 and passes through the point (2, -8).
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The slope of a vertical line is undefined and so there cannot be a slope-intercept form of the equation.
Write an equation in slope-intercept form for the line that passes through the given point and is parallel to the given line (-7,3); x=4
Given a point P = (a,b) and slope m, the equation of a line through P with slope m is (y-b) = m(x-a)
The straight line equation is: y = 2x
Here is how to solve it. First, find the slope of the given line. To do this, solve the equation for "y". That will convert the equation to the slope-intercept form. From there, you can immediately read off the slope. Since parallel lines have the same slope, the line you are looking for will have the same slope. Now you need to use the point-slope form of the equation, with the given point, and the slope you just calculated. Finally, solve this equation for "y" to bring it into the requested slope-intercept form.
You can have infinitely many lines through one specific point, each with a different equation. If you want to have a general equation for ANY line that goes through that point, use the point-slope equation for a line, and use a variable for the slope.
Slope-intercept form
If the equation of a line is in the form ax + by + c = 0 then the slope of the line will be -a/b.
x = 1 (the line intersects the x-axis at 1, and is parallel to the y-axis)We cannot write the equation on the Slope-intercept form, since the slope of the line is undefined. 1 is the x-coordinate of any point on the given line.