Question

question
what is the equation of the line that passes through the point (1, 3) and has a slope of -1?
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.

Step2: Substitute the values

We are given that the point $(x_1,y_1)=(1,3)$ and the slope $m=- 1$. Substituting these values into the point - slope form:
$y - 3=-1(x - 1)$

Step3: Simplify the equation

First, distribute the - 1 on the right - hand side: $y - 3=-x + 1$.
Then, add 3 to both sides of the equation to get the slope - intercept form (or we can leave it in point - slope form, but usually we simplify to slope - intercept form $y=mx + b$).
$y=-x + 1+3$
$y=-x + 4$
We can also write it in standard form $x + y=4$, but the slope - intercept form is also correct.

Answer:

The equation of the line is $y=-x + 4$ (or $x + y=4$ or $y - 3=-1(x - 1)$)