Question

Writing Equations from Point Slope Form into Standard and Slope intercept formM=0; (3, -7)Needs to be taken from point slope form into standard form and slope-intercept form

Answer 1

The equation of the line with a slope of zero and passing through the point (3, -7) is y = -7. This represents a horizontal line, which is the same in both slope-intercept form and standard form.

Step-by-step explanation:

The student is asking how to write an equation in both standard form and slope-intercept form given the slope (m = 0) and a point (3, -7). In the slope-intercept form, the equation of a line is given by y = mx + b, where m is the slope and b is the y-intercept. Since the slope (m) is 0, the line is perfectly horizontal and the equation simply becomes y = b. Since the line passes through the point (3, -7), the value of y is -7 for all values of x, so the equation in slope-intercept form is y = -7.

For the standard form of the equation, which is Ax + By = C, with A, B, and C being integers, the same horizontal line can be expressed as 0x + y = -7 or simply y = -7 after removing the zero term. Therefore, the standard form of the equation is also y = -7.

Answer 2

We are given the following information

Slope = m = 0

Point = (3, -7)

Point-Slope form:

The point-slope form is given by

`(y-y_1)=m(x_{}-x_1)`

Let us substitute the given information into the above formula

`\begin{gathered} (y-(-7)_{})=0\cdot(x_{}-3_{}) \\ (y+7)=0\cdot(x-3) \end{gathered}`

The above equation is written in the point-slope form.

Slope-Intercept form:

The slope-intercept form is given by

`y=mx+b`

Where m is the slope and b is the y-intercept.

We already know the slope, to find the y-intercept, substitute the given point into the equation and solve for b.