Question

lines from point/slope (diagonal only)
score: 6.5/10 penalty: 0.5 off
question
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what is the equation of the line that passes through the point (-5, 5) and has a slope of 3/5?
answer attempt 1 out of 2
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Explanation:

Step1: Recall point - slope form

The point - slope form of a linear equation is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope of the line.
Here, $x_1=- 5$, $y_1 = 5$ and $m=\frac{3}{5}$.

Step2: Substitute values into point - slope form

Substitute $x_1=-5$, $y_1 = 5$ and $m=\frac{3}{5}$ into the formula $y - y_1=m(x - x_1)$:
$y - 5=\frac{3}{5}(x-(-5))$
Simplify the right - hand side: $y - 5=\frac{3}{5}(x + 5)$

Step3: Convert to slope - intercept form (optional, but to get a more standard form)

Distribute the $\frac{3}{5}$ on the right - hand side:
$y-5=\frac{3}{5}x+\frac{3}{5}\times5$
$y - 5=\frac{3}{5}x+3$
Add 5 to both sides of the equation:
$y=\frac{3}{5}x+3 + 5$
$y=\frac{3}{5}x+8$
We can also leave it in point - slope form, but the slope - intercept form is a common way to present the equation of a line.

Answer:

The equation of the line is $y=\frac{3}{5}x + 8$ (or in point - slope form $y - 5=\frac{3}{5}(x + 5)$)