Write the slope-intercept form of the line that has a slope of 2 and intersects the line, 2x - 3y = 6 at x = 3. include your work in your final answer. type your answer in the box provided or use the upload option to submit your solution.

y = 2x-6

Step-by-step explanation:

Slope-intercept form:

The equation of line is given by:

           .....[1]

where, m is the slope and b is the y-intercept.

Given the equation of line:

Since, this line intersects at x = 3.

then;

⇒6 -3y = 6

Subtract 6 from both sides, we have;

0 -3y = 0

or

3y = 0

Divide both sides by 3 we have;

y = 0

⇒Point of intersection = (3, 0)

Substitute the value of x = 3 , y = 0 and slope(m) = 2 in [1] we have;

0 = 2(3)+b

0 = 6+b

Subtract both sides by 6 we have;

-6 = b

or

b = -6

then, we have;

y = 2x-6

Therefore, the the slope-intercept form of the line that has a slope of 2 and intersects the line, 2x - 3y = 6 at x = 3 is, y = 2x-6

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