Question

score: 4/10 penalty: 0.5 off question what is the equation of the line that passes through the point (6, -1) and has a slope of -\frac{3}{2}? answer attempt 1 out of 2

Explanation:

Step1: Recall point - slope form

The point - slope form of a line is given by $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope of the line.
Here, $x_1 = 6$, $y_1=-1$ and $m =-\frac{3}{2}$.

Step2: Substitute values into point - slope form

Substitute the values into the formula: $y-(-1)=-\frac{3}{2}(x - 6)$
Simplify the left - hand side: $y + 1=-\frac{3}{2}(x - 6)$

Step3: Distribute the slope on the right - hand side

Using the distributive property $a(b - c)=ab - ac$, we have $y + 1=-\frac{3}{2}x+(-\frac{3}{2})\times(-6)$
Calculate $(-\frac{3}{2})\times(-6)=9$, so the equation becomes $y + 1=-\frac{3}{2}x + 9$

Step4: Solve for y

Subtract 1 from both sides of the equation: $y=-\frac{3}{2}x+9 - 1$
Simplify the right - hand side: $y=-\frac{3}{2}x + 8$
We can also write this in standard form ($Ax+By = C$) by multiplying through by 2 to get rid of the fraction:
$2y=-3x + 16$
Then, add $3x$ to both sides: $3x+2y = 16$ (either form is correct, but the slope - intercept form $y =-\frac{3}{2}x + 8$ is also a valid equation of the line)

Answer:

The equation of the line is $y=-\frac{3}{2}x + 8$ (or $3x + 2y=16$)