Algebra Equation Picture

Definition of algebra equation picture

           y-y₁=m(x-x₁) where m is the slope and (x₁-y₁) is a point on the straight line in algebra.

     The form is called point-slope form because you use the point and the slope. To write the straight equation of a straight line, you need at least two pieces of information, the slope, and a point on the straight line in algebra. The point on the straight line can be the y-intercept or any other point. Once you have the information, substitute in point-slope form in algebra.

In algebra, slope of the straight line of equation is y-y₁=m(x-x₁)

                

Example problems for algebra equation picture:

Example 1:

         In algebra, write the equation of the straight line equation that passes through the point (3,5) and has a slope of -2.

Solution:

         Substitute x₁=3, y₁=5, and the slope into the point-slope form of the equation of a straight line.

                                    y-y₁=m(x-x₁)

                                    y-5=-2(x-3)

            This y-5=-2(x-3) is an answer to the problem. Sometime you will be asked to give your answer in slope-intercept form. Use the answer you found in point-slope form and change it into slop-intercept form.

                                    y-5=-2(x-3)

                                    y-5=-2x+3

                                       y=-2x+8

            The equation y-5=-2(x-3) in point-slope form is equivalent to y=-2x+8 in slope-intercept form.

                    

Example 2:

            Write the equation of the straight line that passes through the points (3,-2) and (-2,-1). To write the equation of a line, you must have the slope. Find the slope of the straight line using the slope formula.

Solution:

Slope= (Change in y)/(Change in x) = `(y_2-y_1)/(x_2-x_1)`=`(-1+2)/(-2-3)`=`-1/5`

            Use the slope and one of the points in the point-slope form of the equation of the straight line. It does not matter whether you use (3,-2) or (-2,-1). The two answers are equivalent equations.

            y-y₁=m(x-x₁)                                                   y-y₁=m(x-x₁)  

            y+2=`-1/5`(x-3)                                               y+1=`-1/5`(x+2)

            Either y+2=`-1/5`(x-3) or y+1=`-1/5`(x+2) is an acceptable answer if the question does not ask you to give your answer in slope-intercept form. Sometimes you may be asked to give your answer in slope-intercept form.

          y+2=`-1/5`(x-3)                                                 y+1=`-1/5`(x+2)

         y+2=`-1/5`x+`3/5`                                              y+1=`-1/5`x`-2/5`

             y=`-1/5`x+`3/5`-2                                               y=`-1/5`x`-2/5`-1

            y=`-1/5`x+`(3-10)/5`                                            y=`-1/5`x`(-2-5)/5`

            y=`-1/5`x`-7/5`                                                     y=`-1/5`x`-7/5

                      

Practice problems for algebra equation picture:

     Problem 1:

         Write the equation of the straight line passing through the point (-5,2) and (3,4), give your answer in slope-intercept form.

            Answer:          y=`1/4`x+`13/4`

               

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Problem 2:

         Write the equation of a straight line that contains the point (3,3) and has a slope of -2. Write the equation in slope-intercept form.

            Answer:          y=-2x+4