# Graph 3x-4y+16=0

3x-4y+16=0
Solve for y.
Move all terms not containing y to the right side of the equation.
Subtract 3x from both sides of the equation.
-4y+16=-3x
Subtract 16 from both sides of the equation.
-4y=-3x-16
-4y=-3x-16
Divide each term by -4 and simplify.
Divide each term in -4y=-3x-16 by -4.
-4y-4=-3x-4+-16-4
Cancel the common factor of -4.
Cancel the common factor.
-4y-4=-3x-4+-16-4
Divide y by 1.
y=-3x-4+-16-4
y=-3x-4+-16-4
Simplify each term.
Dividing two negative values results in a positive value.
y=(3)x4+-16-4
Divide -16 by -4.
y=3×4+4
y=3×4+4
y=3×4+4
y=3×4+4
Use the slope-intercept form to find the slope and y-intercept.
The slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept.
y=mx+b
Find the values of m and b using the form y=mx+b.
m=34
b=4
The slope of the line is the value of m, and the y-intercept is the value of b.
Slope: 34
y-intercept: 4
Slope: 34
y-intercept: 4
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 0 to substitute in for x to find the ordered pair.
Replace the variable x with 0 in the expression.
f(0)=3(0)4+4
Simplify the result.
Multiply 3 by 0.
f(0)=04+4
Divide 0 by 4.
f(0)=0+4
f(0)=4
4
4
The y value at x=0 is 4.
y=4
y=4
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)4+4
Simplify the result.
Multiply 3 by 1.
f(1)=34+4
To write 4 as a fraction with a common denominator, multiply by 44.
f(1)=34+4⋅44
Combine 4 and 44.
f(1)=34+4⋅44
Combine the numerators over the common denominator.
f(1)=3+4⋅44
Simplify the numerator.
Multiply 4 by 4.
f(1)=3+164
f(1)=194
f(1)=194
194
194
The y value at x=1 is 194.
y=194
y=194
Create a table of the x and y values.
xy041194
xy041194
Graph the line using the slope and the y-intercept, or the points.
Slope: 34
y-intercept: 4
xy041194
Graph 3x-4y+16=0