4y-12=7x

Add 12 to both sides of the equation.

4y=7x+12

Divide each term by 4 and simplify.

Divide each term in 4y=7x+12 by 4.

4y4=7×4+124

Cancel the common factor of 4.

Cancel the common factor.

4y4=7×4+124

Divide y by 1.

y=7×4+124

y=7×4+124

Divide 12 by 4.

y=7×4+3

y=7×4+3

y=7×4+3

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=74

b=3

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

Slope: 74

y-intercept: 3

Slope: 74

y-intercept: 3

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)4+3

Simplify the result.

Multiply 7 by 0.

f(0)=04+3

Divide 0 by 4.

f(0)=0+3

Add 0 and 3.

f(0)=3

The final answer is 3.

3

3

The y value at x=0 is 3.

y=3

y=3

Choose 1 to substitute in for x to find the ordered pair.

Replace the variable x with 1 in the expression.

f(1)=7(1)4+3

Simplify the result.

Multiply 7 by 1.

f(1)=74+3

To write 3 as a fraction with a common denominator, multiply by 44.

f(1)=74+3⋅44

Combine 3 and 44.

f(1)=74+3⋅44

Combine the numerators over the common denominator.

f(1)=7+3⋅44

Simplify the numerator.

Multiply 3 by 4.

f(1)=7+124

Add 7 and 12.

f(1)=194

f(1)=194

The final answer is 194.

194

194

The y value at x=1 is 194.

y=194

y=194

Create a table of the x and y values.

xy031194

xy031194

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

Slope: 74

y-intercept: 3

xy031194

Graph 4y-12=7x