Question

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

Answer 1

`(-(1)/(3),(1)/(2) )` ,
`(-(3)/(2) ,3)`

Explanation:

2y = 3x + 1

y = 2x + 3

Graph 2y = 3x + 1.

Divide each term by 2 and simplify.

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

Rewrite in slope-intercept form.

`y=(3)/(2)x+(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=(3)/(2)`

`b=(1)/(2)`

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

Slope:
`(3)/(2)`

y-intercept:
`(0,(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):
`(-(3)/(2),0 )`

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

Create a table of the x and y values.

_x_|_y_

`-(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_

`-(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):
`(-(3)/(2),0)`

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

Plot each graph on the same coordinate system.