Question

Graph the line with a slope of 2/5 that goes through (3,1)

Answer 1

See attachment and explanation

Explanation:

slope is x/y, which means for each x how many y's it moves by.

so,

2/5 means for every 2 x's it goes up by 5 y's.

so,

you take the point A and go right 2 and go up 5. That's the next point (5,6)

Same with the point other side of A. Go left 2 and go down 5. That's another point (1,-4)

Since, the slope 2/5 is positive, the line will be an increasing line. As shown in the attached image.

Answer 2

`y = (2x)/(5) - (1)/(5)`

Explanation:

Given:

`\bullet \ \ \text{Slope of line:}\ (2)/(5) \\\\ \bullet \ \text{Passes through:} \ (3, 1)`

To determine the equation of the line, we will use point slope form.

Formula of point slope form:

• → y - y₁ = m(x - x₁)

Where "x₁" and "y₁" are the coordinates of the point and "m" is the slope.

Substitute the coordinates and the slope:

`:\implies y - 1 = (2)/(5) (x - 3)`

Simplify the R.H.S:

`:\implies y - 1 = (2x)/(5) - (6)/(5)`

Add 1 both sides:

`:\implies y - 1 + 1 = (2x)/(5) - (6)/(5) + 1`

Simplify the equation:

`:\implies y = (2x)/(5) - (6)/(5) + (5)/(5)`

`:\implies \boxed{y = (2x)/(5) - (1)/(5)}`

Graphing the line on a coordinate plane:

In this case, we are already given a point (3, 1). We can simply plot the y-intercept
`[\bold{(-1)/(5) }]` on the coordinate plane. Then, we can draw a straight line through both points. It is suggested that you use a ruler to do so.

Graph attached**