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charle [14.2K]
2 years ago
15

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

Mathematics
2 answers:
Triss [41]2 years ago
5 0

Answer:

y = \dfrac{2x}{5} - \dfrac{1}{5}

Step-by-step explanation:

Given:

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

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

<u>Formula of point slope form:</u>

  • → 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 = \dfrac{2}{5} (x - 3)

Simplify the R.H.S:

:\implies y - 1 = \dfrac{2x}{5} - \dfrac{6}{5}

Add 1 both sides:

:\implies y - 1 + 1 = \dfrac{2x}{5} - \dfrac{6}{5} + 1

Simplify the equation:

:\implies y = \dfrac{2x}{5} - \dfrac{6}{5} + \dfrac{5}{5}

:\implies \boxed{y = \dfrac{2x}{5} - \dfrac{1}{5}}

<u>Graphing the line on a coordinate plane:</u>

In this case, we are already given a point (3, 1). We can simply plot the y-intercept [\bold{\frac{-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**

Alex73 [517]2 years ago
5 0

Answer:

See attachment and explanation

Step-by-step 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.

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