# Graph 3x-2y=5 3x-2y=5
Solve for y.
Subtract 3x from both sides of the equation.
-2y=5-3x
Divide each term by -2 and simplify.
Divide each term in -2y=5-3x by -2.
-2y-2=5-2+-3x-2
Cancel the common factor of -2.
Cancel the common factor.
-2y-2=5-2+-3x-2
Divide y by 1.
y=5-2+-3x-2
y=5-2+-3x-2
Simplify each term.
Move the negative in front of the fraction.
y=-52+-3x-2
Dividing two negative values results in a positive value.
y=-52+3×2
y=-52+3×2
y=-52+3×2
y=-52+3×2
Rewrite in slope-intercept form.
The slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept.
y=mx+b
Reorder -52 and 3×2.
y=3×2-52
Rewrite in slope-intercept form.
y=32x-52
y=32x-52
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=32
b=-52
The slope of the line is the value of m, and the y-intercept is the value of b.
Slope: 32
y-intercept: -52
Slope: 32
y-intercept: -52
Any line can be graphed using two points. Select two x values, and plug them into the equation to find the corresponding y values.
Choose 1 to substitute in for x to find the ordered pair.
Replace the variable x with 1 in the expression.
f(1)=3(1)2-52
Simplify the result.
Multiply 3 by 1.
f(1)=32-52
Combine the numerators over the common denominator.
f(1)=3-52
Subtract 5 from 3.
f(1)=-22
Divide -2 by 2.
f(1)=-1
-1
-1
The y value at x=1 is -1.
y=-1
y=-1
Choose 3 to substitute in for x to find the ordered pair.
Replace the variable x with 3 in the expression.
f(3)=3(3)2-52
Simplify the result.
Multiply 3 by 3.
f(3)=92-52
Combine the numerators over the common denominator.
f(3)=9-52
Subtract 5 from 9.
f(3)=42
Divide 4 by 2.
f(3)=2
2
2
The y value at x=3 is 2.
y=2
y=2
Create a table of the x and y values.
xy1-132
xy1-132
Graph the line using the slope and the y-intercept, or the points.
Slope: 32
y-intercept: -52
xy1-132
Graph 3x-2y=5     