As extra practice point slope and slope intercept form takes center stage, this opening passage beckons readers into a world crafted with good knowledge, ensuring a reading experience that is both absorbing and distinctly original.

This comprehensive guide delves into the intricacies of linear equations, equipping readers with a thorough understanding of slope-intercept and point-slope forms. Through engaging explanations, practical examples, and ample practice problems, learners will gain a solid foundation in this essential mathematical concept.

Extra Practice: Point-Slope and Slope-Intercept Form: Extra Practice Point Slope And Slope Intercept Form

In this extra practice, we will explore the point-slope form and slope-intercept form of linear equations. We will solve practice problems involving converting between these forms and graphing linear equations.

Point-Slope Form

The point-slope form of a linear equation is:

y

• y₁= m(x
• x ₁)

where (x ₁, y ₁) is a point on the line and m is the slope of the line.

For example, the equation y – 2 = 3(x – 1) is in point-slope form. The point (1, 2) is on the line and the slope is 3.

To convert from point-slope form to slope-intercept form, we solve for y:

y = mx + y₁

mx₁

Slope-Intercept Form

The slope-intercept form of a linear equation is:

y = mx + b

where m is the slope of the line and b is the y-intercept (the value of y when x = 0).

For example, the equation y = 2x + 3 is in slope-intercept form. The slope is 2 and the y-intercept is 3.

To convert from slope-intercept form to point-slope form, we solve for y – y ₁:

y

• y₁= m(x
• x ₁)

Extra Practice Problems, Extra practice point slope and slope intercept form

Equation in Slope-Intercept Form	Equation in Point-Slope Form	Graph of the Equation
y = 2x + 1	y 1 = 2(x 0)	[Gambar grafik garis y = 2x + 1]
y = x + 3	y 3 = 1(x 2)	[Gambar grafik garis y = x + 3]
y = 3x 2	y + 2 = 3(x + 1)	[Gambar grafik garis y = 3x 2]

Solve the following problems:

1. Convert the equation y = 2x + 1 to point-slope form using the point (1, 3).
2. Convert the equation y
   • 3 =
   • 1(x
   • 2) to slope-intercept form.
3. Graph the equation y = 3x
   

   2.

FAQ Guide

What is the difference between slope-intercept form and point-slope form?

Slope-intercept form (y = mx + b) expresses a linear equation in terms of its slope (m) and y-intercept (b), while point-slope form (y – y1 = m(x – x1)) uses a specific point (x1, y1) and the slope to define the line.

How do I convert between slope-intercept form and point-slope form?

To convert from slope-intercept form to point-slope form, substitute the values of m and b into the point-slope formula. To convert from point-slope form to slope-intercept form, solve for y and simplify to the form y = mx + b.

Why is understanding slope-intercept form important?

Slope-intercept form is crucial because it allows us to easily determine the slope and y-intercept of a line, which are essential for graphing, analyzing, and solving linear equations.