Use an equation to find the value of k so that the line that passes through the given points has the given slope. ( 4,−4), (k,−1); slope=34

Using the equation of slope of a straight line, the value of k is 4.09.

Given the following points:

To find the value of k, we would use the equation of slope of a straight line:

Substituting the points and slope into the formula, we have;

Cross-multiplying, we have:

k = 4.09

Therefore, the value of k is 4.09.

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The formula of a slope:

We have the points (4, -4) and (k, -1) and the slope m = 34.

Substitute:

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

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