Question

lines from point/slope (diagonal only)
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 \(x_1 = 6\), \(y_1=-1\) and \(m =-\frac{3}{2}\) into the formula \(y - y_1=m(x - x_1)\):
\(y-(-1)=-\frac{3}{2}(x - 6)\)
Simplify the left - hand side: \(y + 1=-\frac{3}{2}(x - 6)\)

Step3: Distribute the slope

Distribute \(-\frac{3}{2}\) on the right - hand side: \(y+1=-\frac{3}{2}x+(-\frac{3}{2})\times(-6)\)
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: \(y=-\frac{3}{2}x+8\)

Answer:

\(y =-\frac{3}{2}x + 8\) (or in standard form \(3x+2y=16\), but the slope - intercept form is more common here)