# Graph 7x-3y=2 7x-3y=2
Solve for y.
Subtract 7x from both sides of the equation.
-3y=2-7x
Divide each term by -3 and simplify.
Divide each term in -3y=2-7x by -3.
-3y-3=2-3+-7x-3
Cancel the common factor of -3.
Cancel the common factor.
-3y-3=2-3+-7x-3
Divide y by 1.
y=2-3+-7x-3
y=2-3+-7x-3
Simplify each term.
Move the negative in front of the fraction.
y=-23+-7x-3
Dividing two negative values results in a positive value.
y=-23+7×3
y=-23+7×3
y=-23+7×3
y=-23+7×3
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 -23 and 7×3.
y=7×3-23
Rewrite in slope-intercept form.
y=73x-23
y=73x-23
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=73
b=-23
The slope of the line is the value of m, and the y-intercept is the value of b.
Slope: 73
y-intercept: -23
Slope: 73
y-intercept: -23
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 2 to substitute in for x to find the ordered pair.
Replace the variable x with 2 in the expression.
f(2)=7(2)3-23
Simplify the result.
Combine the numerators over the common denominator.
f(2)=7(2)-23
Simplify the numerator.
Multiply 7 by 2.
f(2)=14-23
Subtract 2 from 14.
f(2)=123
f(2)=123
Divide 12 by 3.
f(2)=4
The final answer is 4.
4
4
The y value at x=2 is 4.
y=4
y=4
Choose 0 to substitute in for x to find the ordered pair.
Replace the variable x with 0 in the expression.
f(0)=7(0)3-23
Simplify the result.
Multiply 7 by 0.
f(0)=03-23
Combine the numerators over the common denominator.
f(0)=0-23
Subtract 2 from 0.
f(0)=-23
Move the negative in front of the fraction.
f(0)=-23
The final answer is -23.
-23
-23
The y value at x=0 is -23.
y=-23
y=-23
Create a table of the x and y values.
xy0-2324
xy0-2324
Graph the line using the slope and the y-intercept, or the points.
Slope: 73
y-intercept: -23
xy0-2324
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