Question

1. write an equation for the line that passes through the given point and has the given slope: (6, 2) slope 5

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, $x_1 = 6$, $y_1=2$ and $m = 5$.

Step2: Substitute values into point - slope form

Substitute $x_1 = 6$, $y_1 = 2$ and $m=5$ into the formula $y - y_1=m(x - x_1)$:
$y - 2=5(x - 6)$

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

Expand the right - hand side: $y-2 = 5x-30$
Add 2 to both sides of the equation: $y=5x-30 + 2$
Simplify the right - hand side: $y=5x-28$
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 $y = 5x-28$ (or in point - slope form $y - 2=5(x - 6)$)