Question

line equations from point/slope (point slope form)
score: 4/5 penalty: 1 off
question
use point - slope form to write the equation of a line that passes through the point (7, -5) with slope 1.
answer attempt 1 out of 2
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Explanation:

Step1: Recall point - slope formula

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.

Step2: Identify values

We are given that the point $(x_1,y_1)=(7, - 5)$ and the slope $m = 1$.

Step3: Substitute values into the formula

Substitute $x_1 = 7$, $y_1=-5$ and $m = 1$ into the point - slope formula $y - y_1=m(x - x_1)$.
We get $y-(-5)=1\times(x - 7)$.
Simplify the left - hand side: $y + 5=x - 7$.
We can also leave it in the point - slope form as $y+5 = 1(x - 7)$ or $y+5=(x - 7)$ (since the slope $m = 1$ can be omitted in the multiplication as $1\times(x - 7)=x - 7$).

Answer:

$y + 5=x - 7$ (or $y+5=(x - 7)$ or in slope - intercept form $y=x - 12$)