Question

write the following equation in slope - intercept form and identify the slope and y - intercept. 4x + 3y = 10
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 . (simplify your answer.)
the y - intercept of the line is . (simplify your answer. type an ordered pair.)

Explanation:

Step1: Isolate y - term

Subtract 4x from both sides: $3y=-4x + 10$.

Step2: Solve for y

Divide each term by 3: $y=-\frac{4}{3}x+\frac{10}{3}$.
The slope - intercept form is $y = mx + b$, where m is the slope and b is the y - intercept.

Step3: Identify slope

For $y=-\frac{4}{3}x+\frac{10}{3}$, the slope $m =-\frac{4}{3}$.

Step4: Identify y - intercept

For $y=-\frac{4}{3}x+\frac{10}{3}$, when $x = 0$, $y=\frac{10}{3}$. So the y - intercept is the point $(0,\frac{10}{3})$.

Answer:

The equation in slope - intercept form is $y=-\frac{4}{3}x+\frac{10}{3}$.
The slope of the line is $-\frac{4}{3}$.
The y - intercept of the line is $(0,\frac{10}{3})$.