Write an equation of the line that passes through (0, 5) and (−1.5, 1)

Let's solve this problem step-by-step.

STEP-BY-STEP SOLUTION:

Let's establish the formula we will be using to achieve the equation of the line.

y - y1 = m ( x - x1 )

m = gradient / slope of line

To use the previous formula, we will need to first find the gradient ( m ) using the below formula. We will be substituting the values of the points given in the problem into this formula.

m = ( y2 - y1 ) / ( x2 - x1 )

m = ( 5 - 1 ) / ( 0 - ( - 1.5 ) )

m = ( 5 - 1 ) / ( 0 + 1.5 )

m = 4 / 1.5

m = 8 / 3

Now we will substitute the value of ( m ) from above into the formula for the line. We will also be substituting the values of one of the given points into the formula. In this example, we will be using the point ( 0, 5 ).

y - y1 = m ( x - x1 )

y - 5 = ( 8 / 3 ) ( x - 0 )

y - 5 = ( 8 / 3 )x

y = ( 8 / 3 )x + 5

FINAL ANSWER:

The equation of the line is:

y = ( 8 / 3 )x + 5

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