Question

lines from point/slope (diagonal only)
score 3/10 penalty: 0.5 off
question
what is the equation of the line that passes through the point (-3, 1) and has a slope of -1/3?
answer attempt 2 out of 2

Explanation:

Step1: Recall point - slope form

The point - slope form of a linear equation 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, \(x_1=-3\), \(y_1 = 1\) and \(m=-\frac{1}{3}\).

Step2: Substitute values into point - slope form

Substitute \(x_1=-3\), \(y_1 = 1\) and \(m =-\frac{1}{3}\) into the formula \(y - y_1=m(x - x_1)\):

$$
LATEXBLOCK0
$$

Step3: Simplify the equation

Distribute \(-\frac{1}{3}\) on the right - hand side:

$$
LATEXBLOCK1
$$

Add 1 to both sides of the equation:

$$
LATEXBLOCK2
$$

Or we can also write it in the general form. Starting from \(y - 1=-\frac{1}{3}(x + 3)\), multiply through by 3 to get rid of the fraction:

$$
LATEXBLOCK3
$$

But the slope - intercept form \(y =-\frac{1}{3}x\) is also correct. If we want to write it in the form \(y=mx + b\), we have found that \(b = 0\) after simplification.

Answer:

\(y=-\frac{1}{3}x\) (or \(x + 3y=0\) or \(y-1=-\frac{1}{3}(x + 3)\))