Question

When given Slope= -6/5 Y-intercept= 2 What is this in Point-Slope form?

Answer 1

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Answer:  $\textsf{y - 2 = -6/5(x - 0)}$

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Given:  $\textsf{Slope = -6/5, Goes through (0, 2)}$

Find:  $\textsf{The equation in point-slope form}$

Solution: We need to take the values that were given to us and plug them into the point-slope form.  It doesn't seem like the problem is asking for anything more than that so we will leave it at that.

Plug in the values

• $\textsf{y - y}_1\textsf{ = m(x - x}_1\textsf{)}$

• $\textsf{y - 2 = -6/5(x - 0)}$

Since the problem is just asking for the equation in point-slope form the final expression would be y - 2 = -6/5(x - 0).

Answer 2

Answer:

$\sf y - 2 = -\dfrac{6}{5}(x - 0)$

Step-by-step explanation:

$\sf \large \underline{\textsf{Given:}}\ \textsf{a line with a slope of -\dfrac{6}{5} , and a y-intercept of 2 }$

We're given a y-intercept of 2, but using the slope-intercept form, we can immediately determine that x = 0. Hence, the given point is (0, 2).

Then, we substitute these values into the Point-Slope Form to find the equation.

Here are both forms for future reference:

⇒ Slope-Intercept Form: y = mx + b

[ Where: m is the slope, and b is the y-intercept (when x = 0). ]

⇒ Point-Slope Form: y - y₁ = m(x - x₁)

[ Where: m is the slope, and (x₁, y₁) is a given point. ]

Substitute the values into the Point-Slope Form:

$\sf\\\implies y - y_1 = m(x - x_1)\\\\\implies y - 2 = -\dfrac{6}{5}(x - 0)$

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