Question

write the following equation in slope - intercept form and identify the slope and y - intercept. 6x + 7y = 12. the equation in slope - intercept form is y = . (simplify your answer. type in the form y = mx + b. use integers or fractions for any numbers in the expression). the slope of the line is 12 (simplify your answer.). the y - intercept of the line is . (simplify your answer. type an ordered pair.)

Explanation:

Step1: Isolate y - term

Subtract 6x from both sides of 6x + 7y = 12: 7y=-6x + 12

Step2: Solve for y

Divide each term by 7: $y=-\frac{6}{7}x+\frac{12}{7}$
The slope - intercept form is y = mx + b, where m is the slope and b is the y - intercept.

Step3: Identify slope

Comparing $y=-\frac{6}{7}x+\frac{12}{7}$ with y = mx + b, the slope $m =-\frac{6}{7}$

Step4: Identify y - intercept

The y - intercept occurs when x = 0. In the form y = mx + b, the y - intercept is the point (0,b). Here, $b=\frac{12}{7}$, so the y - intercept is the point $(0,\frac{12}{7})$

Answer:

The equation in slope - intercept form is $y =-\frac{6}{7}x+\frac{12}{7}$
The slope of the line is $-\frac{6}{7}$
The y - intercept of the line is $(0,\frac{12}{7})$