Question

what is the point-slope equation for y=2x+3

Answer 1

ANSWER TO QUESTION NO #83626 – MATH – ALGEBRA

QUESTION

What is the point-slope equation for $y = 2x + 3$

ANSWER

DEFINITION OF POINT-SLOPE FORM:

It is line geometry function mathematically defined by the formula $y - y1 = m(x - x1)$. It illustrates that the difference between the two points $(y - y1)$ of 'y' coordinate on a line is proportional to the difference between the two points $(x - x1)$ of 'x' coordinate on a line.

'm' is the slope of a line

$(x1, y1)$ is any point on a line

FORMULA: The formula which is used to find the point-slope form of a line

$$(y - y1) = m(x - x1)$$

'm' is the slope of a line

$(x1, y1)$ is any point on a line

SOLUTION

In this question the equation of the line is $y = 2x + 3$

'm' = 2, the slope of the line

So, for this question the equation can written in this form,

$$y = 2x + 4 - 1$$ $$y = 2(x + 2) - 1$$ $$y + 1 = 2(x + 2)$$ $$y - (-1) = 2(x + 2)$$

So, a point-slope form of this equation can be written as $y - (-1) = 2(x + 2)$

The point-slope form of this equation can be written in this way also-

$$y = 2x + 3$$ $$y = 2\left(x + \frac{3}{2}\right)$$ $$y - 0 = 2\left(x - \left(-\frac{3}{2}\right)\right)$$

Thus, for different coordinates different point-slope form can be formed. Two point-slope forms which I am producing here are

$$y - (-1) = 2(x - (-2)) \text{ (ANSWER)}$$ $$y - 0 = 2\left(x - \left(-\frac{3}{2}\right)\right) \quad \text{ (ANSWER)}$$

For the first point-slope form coordinate on the line is, $(-2, -1)$

$2^{\text{nd}}$ point-slope form coordinate on the line is, $(-3/2, 0)$

Try to evaluate other point-slope form which can be formed for different coordinates on the line.

Another point-slope form which can be formed is

$$y = 2x + 3$$ $$y = 2x + 6 - 3$$ $$y - (-3) = 2(x - (-3)) \text{ (ANSWER)}$$

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