# What is the equation of the line in slope-intercept form, that passes through a given point and which is parallel to a given line. For example: (-3,-4);2y=4+3x , (5,-1);y=-3/5x-3 , (9,4);y-x=3...

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

You are allowed to ask only one question at a time, I have edited your question to comply with the same.

Any problem where you want to find the equation of a line in slope-intercept form which is parallel to a given line and which passes through a given point can be solved in the following way.

Let the point that is given be (a1, b1) and let the line be y = mx + c

As two parallel lines have the same slope the line you get will have the slope m. The line also has to pass through (a1, b1). It can be written as: (y - b1)/(x - a1) = m

=> y - b1 = mx - m*a1

=> y = mx + ( b1 - m*a1)

This is the equation of the line in slope-intercept form that passes through (a1, b1) and is parallel to y = mx + c.

In the problems you are given substitute the values of m, a1 and b1  you get the required equation.

tubbycat117 | Student, Grade 9 | eNotes Newbie

Posted on

In slope-Intercept form, that passes through the given point and is perpendicular* to the given line.

(5,-8);y=5/2x+4

(2,-3);6y=-2x+1

(-5,2);y+3=2x

(7,10);y=0.5x-9

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