Writing Equation of Line in Slope Intercept Form

Find the Equations of the Lines in Slope- Intercept Form

• The line passes through (-1,3) and (-4,5)

• The line with slope -2.5 and passes through (2,1.5)

• The Line passes through (1,6) and (0,5)

• The Line passes through (1,-1) and (5,3)

• The line with a constant of 5 and passing through (1,7)

Equation of the Line passing through (-1,3) and (-4,5)

Y = mx + c

We determine the gradient of the line to find value the value of m.

Gradient = y2/x2 - y1/x1

Where (x1, y1) = (-1,3) and (x2, y2) = (-4,5)

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Y = -2/3 x + c

5 = - 2/3 (-4) + c

The value of c = 5 - 8/3 = 7/3 

Therefore, the equation of the line passing through (-1,3) and (-4,5) is y = -2/3 x + 7/3

Equation of the line with slope -2.5 and passing through (2,1.5)

We know the values of y = mx + c where m is gradient and c is the constant value of in the line graph.

Therefore, y = 1.5, m = -2.5 and x = 2.

We can the find the value of c using the values provided in the question.

1.5 = -2.5 x 2 + c

1.5 = -5 + c

c = 1.5 + 5

c = 6.5

Therefore, the equation of the line with slope -2.5 and passing through (2,1.5) is y = -2.5 x + 6.5.  

Equation of the Line passing through (1,6) and (0,5)

The value of y = mx + c. We can utilize the coordinates provided to find the gradient of the line described.

Gradient (m) = y2/x1 – y2/x1

Gradient (m) = 6/1 – 5/0

The value of the slope is = 1

If the slope is 1, the variable c is can be calculated using the one point in the line graph.

6 = 1 x1 + c

c = 5

Hence, the equation of line passing through (1,6) and (0,5) is y = x + 5.

Equation of the Line passing through (1,-1) and (5,3)

We use y = mx+c to determine the value of each point in the graph.

Gradient/Slope of the line (m) = y2/x2 – y1/y2

Gradient = 3/5 – -1/1 

Gradient = 4/4

Gradient of the line (m) = 1

We use point (5,3) to compute the constant c variable.

y = 3 while x = 5 and m = 1

Therefore, we have 3 = 5 + c.

c = 3- 5 = -2

Thus, the equation of line passing through (1,-1) and (5,3) is y = x - 2.

Equation of the Line with a constant of 5 and passing through (1,7)

To do this algebraic task, we can still use y = mx +c in order to find the equation of the line passing through (1,7) where the constant value in the vertical axis is 5.

The value of y is 7 while x = 1 and c = 5.

M x 1 + 5 = 7 -> M = 7 – 5

If the value of the gradient is 2 and c = 5, then the equation is y = 2x + 5.