Find the slope and $y$-intercept of the graph of this linear equation.
y-3 x=-6
slope:
$y$-intercept: $\square$
Answer (2)
Rewrite the given equation y − 3 x = − 6 in slope-intercept form.
Isolate y by adding 3 x to both sides, resulting in y = 3 x − 6 .
Identify the slope as the coefficient of x , which is 3 .
Identify the y -intercept as the constant term, which is − 6 .
Explanation
Understanding the Problem We are given the linear equation y − 3 x = − 6 and asked to find the slope and y -intercept of its graph. To do this, we need to rewrite the equation in slope-intercept form, which is y = m x + b , where m represents the slope and b represents the y -intercept.
Converting to Slope-Intercept Form To convert the given equation to slope-intercept form, we need to isolate y on one side of the equation. We can do this by adding 3 x to both sides of the equation:
y − 3 x + 3 x = − 6 + 3 x
This simplifies to:
y = 3 x − 6
Identifying Slope and Intercept Now that the equation is in the form y = m x + b , we can easily identify the slope and y -intercept.
The slope, m , is the coefficient of x , which is 3 .
The y -intercept, b , is the constant term, which is − 6 .
Stating the Answer Therefore, the slope of the line is 3 and the y -intercept is − 6 .
Examples
Understanding slope and y-intercept is crucial in many real-world applications. For example, imagine you are tracking the cost of a taxi ride. The initial fee could be represented by the y-intercept, and the cost per mile driven could be represented by the slope. If the initial fee is $3 and the cost per mile is 2 , t h ee q u a t i o n w o u l d b e y = 2x + 3$. This equation helps you predict the total cost of the ride based on the distance traveled.
The slope of the line is 3, and the y-intercept is -6. This means that the line increases by 3 units in the y-direction for every 1 unit it moves in the x-direction, intersecting the y-axis at -6. The equation of the line can be expressed in slope-intercept form as y = 3x - 6.
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