Question

line equations from point/slope
question
what is the equation of the line that passes through the point (1, 1) and has a slope of -5?
answer
attempt 1 out of 2

Explanation:

Step1: Recall point - slope formula

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.

Step2: Substitute the values

We are given that the point $(x_1,y_1)=(1,1)$ and the slope $m = - 5$. Substituting these values into the point - slope formula, we get:
$y - 1=-5(x - 1)$

Step3: Simplify the equation

First, distribute the - 5 on the right - hand side:
$y - 1=-5x+5$
Then, add 1 to both sides of the equation to solve for $y$:
$y=-5x + 5+1$
$y=-5x+6$
We can also write it in the standard form $Ax + By=C$. Starting from $y=-5x + 6$, add $5x$ to both sides:
$5x+y=6$

Answer:

The equation of the line is $y=-5x + 6$ (or $5x + y=6$)