Understanding the Slope of the Line 3x – 6y = 12
Ahoy, mathmatey! Avast ye as we set sail on the high seas of algebra to unravel the mysteries of slopes and intercepts! Let’s dive into understanding the slope of the line 3x – 6y = 12, arrr!
Ye see, when a line be given in a form like 3x – 6y = 12, finding the slope be akin to hunting for buried treasure. Ye start by isolating y just like spotting a hidden X on a map. By rearranging the equation to solve for y, ye’ll see that the slope be 1/2. Aye, that’s right – if this were a ship, it would sail at a steady pace of 1/2 along the y-axis for every unit it moves on the x-axis.
Now me hearty, let’s not forget about the y-intercept! It be like findin’ land after a long voyage. For this line, 3x + 2y = 12, when ye let x = 0 and solve for y, ye find that the ship crosses the y-axis at (0, -6). That point be where yer journey starts on the vertical axis.
Arrr me mateys! Don’t sail away just yet; there be more treasures to uncover in the depths of algebraic seas. Keep yer eyes peeled and continue readin’ to discover more about slopes and intercepts! Onward we go!
Finding the Y-Intercept of the Line 3x – 6y = 12
To find the y-intercept of the line 3x – 6y = 12, you can start by converting the equation to slope-intercept form, y = mx + b. The slope-intercept form helps easily identify the slope, denoted by ‘m,’ and the y-intercept represented by ‘b.’ By isolating ‘y’ in this equation, you will have y = (1/2)x – 2. Here, the slope, which tells you how steep or flat a line is, is 1/2 (m = 1/2), indicating that for each unit moved along the x-axis, the line rises or falls by half a unit. The y-intercept for this line is -2; this means that the line crosses the y-axis at point (0, -2), resembling where your algebraic voyage begins vertically.
Now, let’s delve deeper into finding slopes and intercepts like true algebraic pirates! Remember that when tackling equations like 3x + 6y = 12 or similar variations such as finding slopes from equations like 6x – 3y = 12 or figuring out different slopes and intercepts based on specific configurations like in y = -12x + 2; you must sail through rearranging equations to spot hidden treasures like slopes and intercepts. It’s like deciphering complex maps where numbers lead you to coordinates revealing valuable insights about lines on mathematical maps.
Moreover, knowing how to convert equations into their slope-intercept form makes navigating algebraic seas much smoother. By following simple steps like isolating ‘y’ and identifying coefficients accurately using proper formulas helps in unraveling mathematical mysteries with dexterity. Imagine transforming cryptic equations into straightforward formulas akin to cracking codes on a treasure map – each step leading closer to discovering hidden gems of knowledge buried within algebraic expressions.
So next time you set sail on the turbulent waters of algebra seeking treasures of slopes and intercepts, remember these handy maneuvers to navigate smoothly through mathematical equations. Keeping a keen eye out for clues embedded within formulas will surely lead you to conquer challenging algebraic problems with ease – just like a seasoned captain navigating rough seas with finesse! Onward mathmateys, adventure awaits in every formula and every graph!
What is the slope of the line 3x 6y 12?
The slope of the line 3x 6y 12 is 1/2.
What is the y-intercept of the line 3x 2y 12?
The y-intercept of the line 3x 2y 12 is (0,6).
Which of the following is the solution of the equation 2x y 2?
The solution of the equation 2x y 2 is (3,4).
What is a linear equation in 2 variables?
An equation is a linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y are not equal to zero.