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 $-\frac{1}{4}$?

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, \(x_1=- 3\), \(y_1 = 1\) and \(m=-\frac{1}{4}\).

Step2: Substitute values into point - slope form

Substitute \(x_1=-3\), \(y_1 = 1\) and \(m =-\frac{1}{4}\) into the formula \(y - y_1=m(x - x_1)\):
\(y - 1=-\frac{1}{4}(x-(-3))\)
Simplify the right - hand side: \(y - 1=-\frac{1}{4}(x + 3)\)

Step3: Convert to slope - intercept form (optional, but common)

Distribute the \(-\frac{1}{4}\) on the right - hand side:
\(y-1=-\frac{1}{4}x-\frac{3}{4}\)
Add 1 to both sides. Since \(1=\frac{4}{4}\), we have:
\(y=-\frac{1}{4}x-\frac{3}{4}+\frac{4}{4}\)
\(y=-\frac{1}{4}x+\frac{1}{4}\)
We can also leave it in point - slope form: \(y - 1=-\frac{1}{4}(x + 3)\)

Answer:

The equation of the line in point - slope form is \(y - 1=-\frac{1}{4}(x + 3)\) and in slope - intercept form is \(y=-\frac{1}{4}x+\frac{1}{4}\)