# How do you use the point on the line and the slope of the line to find three additional points through which the line passes: Point: (5, -6) Slope: m = 1?

Aug 8, 2017

(0,-11), (4,-7) and (6,-5)

#### Explanation:

We first must construct a linear equation from which these point will lie on. This can be done using the formula

$\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)$

$m$ would be the gradient of the graph, which we have; $m = 1$

${x}_{1} \mathmr{and} {y}_{1}$ are a point on the graph, which we are given; ${x}_{1} = 5$ and ${y}_{1} = - 6$

Thus, we will get a linear equation of

$\left(y - \left(- 6\right)\right) = 1 \left(x - \left(5\right)\right)$

$\left(y + 6\right) = \left(x - 5\right)$

$y = x - 11$

graph{y=x-11 [-17.41, 22.59, -15.04, 4.96]}

Now, we can substitute values for x and y to find 3 additional points that lie on this line.