Question

solve for x and y graphically, 2y= 3x+1 and y=2x+3

Answer 1

Answer:

$(-\frac{1}{3},\frac{1}{2} )$ , $(-\frac{3}{2} ,3)$

Step-by-step explanation:

2y = 3x + 1

y = 2x + 3

Graph 2y = 3x + 1.

Divide each term by 2 and simplify.

      $y=\frac{3x}{2}+\frac{1}{2}$

Rewrite in slope-intercept form.

      $y=\frac{3}{2}x+\frac{1}{2}$

Use the slope-intercept form to find the slope and y-intercept.

Find the values of m and b using the form y = mx + b.

       $m=\frac{3}{2}$

        $b=\frac{1}{2}$

The slope of the line is the value of m, and the y-intercept is the value of b.

Slope: $\frac{3}{2}$

y-intercept: $(0,\frac{1}{2} )$

Any line can be graphed using two points. Select two x values, and plug them into the  equation to find the corresponding y values.

Find the x-intercept.

x-intercept(s):  $(-\frac{3}{2},0 )$

y-intercept(s): (0, 3)

Create a table of the x and y values.

  _x_|_y_

  $-\frac{3}{2}$  |   $0$

     $0$  |   $3$

Graph the line using the slope and the y-intercept, or the points.

Slope: 2

intercept: (0, 3)

  _x_|_y_

  $-\frac{3}{2}$  |   $0$

     $0$  |   $3$

Graph y = 2x + 3

Use the slope-intercept form to find the slope and y-intercept.

Slope: 2

intercept: (0, 3)

x-intercept(s): $(-\frac{3}{2},0)$

y-intercept(s): (0, 3)

Plot each graph on the same coordinate system.